Question 1

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 9 } { 2 } x$

Accepted Answer

A) vertex: (0,0)focus: $$\left( - \frac { 9 } { 8 } , 0 \right)$$ 
B) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 9 } { 2 } , - \frac { 9 } { 2 } \right)$ 
C) vertex: (0,0)focus: $\left( 0 , - \frac { 9 } { 2 } \right)$ 
D) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $$\left( 0 , - \frac { 9 } { 8 } \right)$$ 
E) vertex: (0,0)focus: $\left( - \frac { 9 } { 2 } , 0 \right)$ 
A) vertex: (0,0)focus: $$\left( - \frac { 9 } { 8 } , 0 \right)$$ 
B) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 9 } { 2 } , - \frac { 9 } { 2 } \right)$ 
C) vertex: (0,0)focus: $\left( 0 , - \frac { 9 } { 2 } \right)$ 
D) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $$\left( 0 , - \frac { 9 } { 8 } \right)$$ 
E) vertex: (0,0)focus: $\left( - \frac { 9 } { 2 } , 0 \right)$

Question 2

Find the standard form of the equation of the ellipse with the following graph.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 0$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 0$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 0$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 100$ , $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $25 x ^ { 2 } + 4 y ^ { 2 } = 1$ , $\frac { x ^ { 2 } } { 2 } - \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } - y ^ { 2 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1$ , $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } + y ^ { 2 } = 1$ 
A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 0$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 0$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 0$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 100$ , $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $25 x ^ { 2 } + 4 y ^ { 2 } = 1$ , $\frac { x ^ { 2 } } { 2 } - \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } - y ^ { 2 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1$ , $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } + y ^ { 2 } = 1$

Question 3

Give the coordinates of the circle's center and its radius.​ $$( x - 6 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4$$ ​

Accepted Answer

A) (-6,5);r = 4 
B) (6,-5);r = 2 
C) (6,-5);r = 4 
D) (-6,5);r = 2 
E) none of these 
A) (-6,5);r = 4 
B) (6,-5);r = 2 
C) (6,-5);r = 4 
D) (-6,5);r = 2 
E) none of these

Question 4

A simply supported beam is 12 meters long and has a load at the center (see figure).​   ​ where, $a = 12 , b = 2$ The deflection of the beam at its center is 2 centimeters.Assume that the shape of the deflected beam is parabolic.Write an equation of the parabola.(Assume that the origin is at the center of the deflected beam. )
​

Accepted Answer

A)  $$x ^ { 2 } = - 180 y$$ 
B)  $$x ^ { 2 } = 180 y$$ 
C)  $y ^ { 2 } = 180 x$ 
D)  $y ^ { 2 } = - 180,000 x$ 
E)  $x ^ { 2 } = 180,000 y$ 
A)  $$x ^ { 2 } = - 180 y$$ 
B)  $$x ^ { 2 } = 180 y$$ 
C)  $y ^ { 2 } = 180 x$ 
D)  $y ^ { 2 } = - 180,000 x$ 
E)  $x ^ { 2 } = 180,000 y$

Question 5

Select the graph of the following equation.​ $$x ^ { 2 } = 8 y$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 6

Find the vertex and focus of the parabola. $$y ^ { 2 } = - \frac { 3 } { 4 } x$$

Accepted Answer

A) vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $\left( - \frac { 3 } { 4 } , - \frac { 3 } { 4 } \right)$ 
B) vertex: (0,0)focus: $\left( 0 , - \frac { 3 } { 4 } \right)$ 
C) vertex: (0,0)focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ 
D) vertex: (0,0)focus: $\left( - \frac { 3 } { 16 } , 0 \right)$ 
E) vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $$\left( 0 , - \frac { 3 } { 16 } \right)$$ 
A) vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $\left( - \frac { 3 } { 4 } , - \frac { 3 } { 4 } \right)$ 
B) vertex: (0,0)focus: $\left( 0 , - \frac { 3 } { 4 } \right)$ 
C) vertex: (0,0)focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ 
D) vertex: (0,0)focus: $\left( - \frac { 3 } { 16 } , 0 \right)$ 
E) vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $$\left( 0 , - \frac { 3 } { 16 } \right)$$

Question 7

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( 0 , \frac { 1 } { 2 } \right)$

Accepted Answer

A)  $x ^ { 2 } = \frac { 2 } { 4 } y$ 
B)  $y ^ { 2 } = \frac { 2 } { 4 } x$ 
C)  $y ^ { 2 } = \frac { 4 } { 2 } x$ 
D)  $x ^ { 2 } = \frac { 4 } { 2 } y$ 
E)  $y ^ { 2 } = x$ 
A)  $x ^ { 2 } = \frac { 2 } { 4 } y$ 
B)  $y ^ { 2 } = \frac { 2 } { 4 } x$ 
C)  $y ^ { 2 } = \frac { 4 } { 2 } x$ 
D)  $x ^ { 2 } = \frac { 4 } { 2 } y$ 
E)  $y ^ { 2 } = x$

Question 8

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (0,±2);asymptotes: y = ± $\frac { 3 } { 2 }$ x
​

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 4 } = 1$ 
B)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 4 } = - 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ 
E)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 4 } = 1$ 
A)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 4 } = 1$ 
B)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 4 } = - 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ 
E)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 4 } = 1$

Question 9

The revenue R (in dollars)generated by the sale of x units of a patio furniture set is given by $( x - 116 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 16,820 )$ .Approximate the number of sales that will maximize revenue. ​

Accepted Answer

A)  $$R = 116 x - \frac { 5 } { 4 } x ^ { 2 }$$ The revenue is maximum when $x = 116$ units. 
B)  $R = 116 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units. 
C)  $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units. 
D)  $R = 290 x - \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 116$ units. 
E)  $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 290$ units. 
A)  $$R = 116 x - \frac { 5 } { 4 } x ^ { 2 }$$ The revenue is maximum when $x = 116$ units. 
B)  $R = 116 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units. 
C)  $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units. 
D)  $R = 290 x - \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 116$ units. 
E)  $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 290$ units.

Question 10

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0,-4)

Accepted Answer

A) x2 = -16y 
B) x2 = -4y 
C) x2 = 4y 
D) y2 = -16x 
E) y2 = -4x 
A) x2 = -16y 
B) x2 = -4y 
C) x2 = 4y 
D) y2 = -16x 
E) y2 = -4x

Question 11

Find the vertex,focus,and directrix of the parabola.​ $x ^ { 2 } + 4 y = 0$ ​

Accepted Answer

A) Vertex: (0,0);Focus: $\left( \frac { 1 } { 4 } , 0 \right)$ ;Directrix: $y = \frac { 1 } { 4 }$ 
B) Vertex: (0,0);Focus: $\left( - \frac { 1 } { 4 } , 0 \right)$ ;Directrix: $y = \frac { 1 } { 4 }$ 
C) Vertex: (0,0): Focus: $\left( 0 , \frac { 4 } { 4 } \right)$ Directrix: $y = - \frac { 4 } { 4 }$ 
D) Vertex: (0,0);Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ;Directrix: $y = \frac { 4 } { 4 }$ 
E) Vertex: (0,0);Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ;Directrix: $y = - \frac { 4 } { 4 }$ 
A) Vertex: (0,0);Focus: $\left( \frac { 1 } { 4 } , 0 \right)$ ;Directrix: $y = \frac { 1 } { 4 }$ 
B) Vertex: (0,0);Focus: $\left( - \frac { 1 } { 4 } , 0 \right)$ ;Directrix: $y = \frac { 1 } { 4 }$ 
C) Vertex: (0,0): Focus: $\left( 0 , \frac { 4 } { 4 } \right)$ Directrix: $y = - \frac { 4 } { 4 }$ 
D) Vertex: (0,0);Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ;Directrix: $y = \frac { 4 } { 4 }$ 
E) Vertex: (0,0);Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ;Directrix: $y = - \frac { 4 } { 4 }$

Question 12

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±4)focies: (0,±5)

Accepted Answer

A)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 25$ 
E)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 25$ 
E)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 25 } = 1$

Question 13

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( 0 , - 4 )$

Accepted Answer

A)  $x ^ { 2 } = 16 y$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 16 x$ 
D)  $x ^ { 2 } = - 16 y$ 
E)  $y ^ { 2 } = - 16 x$ 
A)  $x ^ { 2 } = 16 y$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 16 x$ 
D)  $x ^ { 2 } = - 16 y$ 
E)  $y ^ { 2 } = - 16 x$

Question 14

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -5
​

Accepted Answer

A) y2 = 20x 
B) y2 = -5x 
C) x2 = -20y 
D) x2 = -5y 
E) x2 = 20y 
A) y2 = 20x 
B) y2 = -5x 
C) x2 = -20y 
D) x2 = -5y 
E) x2 = 20y

Question 15

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 1 } { 7 } x$

Accepted Answer

A) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $$\left( 0 , - \frac { 1 } { 28 } \right)$$ 
B) vertex: $\left( 0 , \frac { 5 } { 4 } \right)$ focus: $$\left( - \frac { 1 } { 7 } , - \frac { 1 } { 7 } \right)$$ 
C) vertex: (0,0)focus: $\left( - \frac { 1 } { 28 } , 0 \right)$ 
D) vertex: (0,0)focus: $\left( - \frac { 1 } { 7 } , 0 \right)$ 
E) vertex: (0,0)focus: $\left( 0 , - \frac { 1 } { 7 } \right)$ 
A) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $$\left( 0 , - \frac { 1 } { 28 } \right)$$ 
B) vertex: $\left( 0 , \frac { 5 } { 4 } \right)$ focus: $$\left( - \frac { 1 } { 7 } , - \frac { 1 } { 7 } \right)$$ 
C) vertex: (0,0)focus: $\left( - \frac { 1 } { 28 } , 0 \right)$ 
D) vertex: (0,0)focus: $\left( - \frac { 1 } { 7 } , 0 \right)$ 
E) vertex: (0,0)focus: $\left( 0 , - \frac { 1 } { 7 } \right)$

Question 16

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.​ $$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$$ ​

Accepted Answer

A) Center: (0,0) Vertices: (-6,0)
​   
B) Center: (0,0) Vertices: (±6,0)
​   
C) Center: (0,0) Vertices: (-6,0)
​   
D) Center: (0,0) Vertices: (±6,0)
​   
E) Center: (0,0) Vertices: (6,0)
​   
A) Center: (0,0) Vertices: (-6,0)
​   
B) Center: (0,0) Vertices: (±6,0)
​   
C) Center: (0,0) Vertices: (-6,0)
​   
D) Center: (0,0) Vertices: (±6,0)
​   
E) Center: (0,0) Vertices: (6,0)
​

Question 17

Find the vertex,focus,and directrix of the parabola.​ $( x - 1 ) ^ { 2 } + 16 ( y + 6 ) = 0$ ​

Accepted Answer

A) Vertex: $( 0 , - 4 )$ ;Focus: $( 1 , - 6 )$ ;Directrix: $y = 0$ 
B) Vertex: $( 1 , - 10 )$ ;Focus: $( 1 , - 10 )$ ;Directrix: $y = 0$ 
C) Vertex: $( - 4,1 )$ ;Focus: $( - 4,1 )$ ;Directrix: $y = 0$ 
D) Vertex: $( 1 , - 6 )$ ;Focus: $( 1 , - 10 )$ ;Directrix: $y = 0$ 
E) Vertex: $( 1 , - 6 )$ ;Focus: $( 1 , - 4 )$ ;Directrix: $y = 6$ 
A) Vertex: $( 0 , - 4 )$ ;Focus: $( 1 , - 6 )$ ;Directrix: $y = 0$ 
B) Vertex: $( 1 , - 10 )$ ;Focus: $( 1 , - 10 )$ ;Directrix: $y = 0$ 
C) Vertex: $( - 4,1 )$ ;Focus: $( - 4,1 )$ ;Directrix: $y = 0$ 
D) Vertex: $( 1 , - 6 )$ ;Focus: $( 1 , - 10 )$ ;Directrix: $y = 0$ 
E) Vertex: $( 1 , - 6 )$ ;Focus: $( 1 , - 4 )$ ;Directrix: $y = 6$

Question 18

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.   L = 5 inches

Accepted Answer

A)  $y = 5 x ^ { 2 }$ 
B)  $x ^ { 2 } = 5 y$ 
C)  $y = 20 x ^ { 2 }$ 
D)  $x ^ { 2 } = 20 y$ 
E) ​ $y = \frac { 1 } { 5 } x ^ { 2 }$ 
A)  $y = 5 x ^ { 2 }$ 
B)  $x ^ { 2 } = 5 y$ 
C)  $y = 20 x ^ { 2 }$ 
D)  $x ^ { 2 } = 20 y$ 
E) ​ $y = \frac { 1 } { 5 } x ^ { 2 }$

Question 19

Find the vertex,focus,and directrix of the parabola.​ $( x + 3 ) + ( y - 1 ) ^ { 2 } = 0$ ​

Accepted Answer

A) Vertex: $( - 3,1 )$ ;Focus: $\left( \frac { - 13 } { 4 } , 1 \right)$ ;Directrix: $x = \frac { - 11 } { 4 }$ 
B) Vertex: $( 1 , - 3 , )$ ;Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$ 
C) Vertex: $( 1 , - 3 , )$ ;Focus: $\left( \frac { - 11 } { 4 } , 1 \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$ 
D) Vertex: $( - 3,1 )$ ;Focus: $\left( 1 , \frac { - 13 } { 4 } \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$ 
E) Vertex: $( - 3,1 )$ ;Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$ 
A) Vertex: $( - 3,1 )$ ;Focus: $\left( \frac { - 13 } { 4 } , 1 \right)$ ;Directrix: $x = \frac { - 11 } { 4 }$ 
B) Vertex: $( 1 , - 3 , )$ ;Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$ 
C) Vertex: $( 1 , - 3 , )$ ;Focus: $\left( \frac { - 11 } { 4 } , 1 \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$ 
D) Vertex: $( - 3,1 )$ ;Focus: $\left( 1 , \frac { - 13 } { 4 } \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$ 
E) Vertex: $( - 3,1 )$ ;Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$

Question 20

The path of a projectile projected horizontally with a velocity of v feet per second at a height of s feet,where the model for the path is $$x ^ { 2 } = - \frac { v ^ { 2 } } { 16 } ( y - s )$$ .In this model (in which air resistance is disregarded),y is the height (in feet)of the projectile and x is the horizontal distance (in feet)the projectile travels.A ball is thrown from the top of a 150-foot tower with a velocity of 32 feet per second.Find the equation of the parabolic path. ​

Accepted Answer

A)  $x ^ { 2 } = - 32 ( y - 150 )$ 
B)  $x ^ { 2 } = 64 ( y - 150 )$ 
C)  $x ^ { 2 } = 1406 ( y - 32 )$ 
D)  $x ^ { 2 } = - 1406 ( y - 32 )$ 
E)  $x ^ { 2 } = - 64 ( y - 150 )$ 
A)  $x ^ { 2 } = - 32 ( y - 150 )$ 
B)  $x ^ { 2 } = 64 ( y - 150 )$ 
C)  $x ^ { 2 } = 1406 ( y - 32 )$ 
D)  $x ^ { 2 } = - 1406 ( y - 32 )$ 
E)  $x ^ { 2 } = - 64 ( y - 150 )$

Exam 60: Introduction to Conics Parabolas

Find the vertex and focus of the parabola. y2=−92xy ^ { 2 } = - \frac { 9 } { 2 } xy2=−29​x

Find the standard form of the equation of the ellipse with the following graph.

Give the coordinates of the circle's center and its radius.​ (x−6)2+(y+5)2=4( x - 6 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4(x−6)2+(y+5)2=4 ​

Select the graph of the following equation.​ x2=8yx ^ { 2 } = 8 yx2=8y ​

Find the vertex and focus of the parabola. y2=−34xy ^ { 2 } = - \frac { 3 } { 4 } xy2=−43​x

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: (0,12)\left( 0 , \frac { 1 } { 2 } \right)(0,21​)

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​ Vertices: (0,±2);asymptotes: y = ± 32\frac { 3 } { 2 }23​ x ​

The revenue R (in dollars)generated by the sale of x units of a patio furniture set is given by (x−116)2=−45(R−16,820)( x - 116 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 16,820 )(x−116)2=−54​(R−16,820) .Approximate the number of sales that will maximize revenue. ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0,-4)

Find the vertex,focus,and directrix of the parabola.​ x2+4y=0x ^ { 2 } + 4 y = 0x2+4y=0 ​

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±4)focies: (0,±5)

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: (0,−4)( 0 , - 4 )(0,−4)

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -5 ​

Find the vertex and focus of the parabola. y2=−17xy ^ { 2 } = - \frac { 1 } { 7 } xy2=−71​x

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.​ x236+y29=1\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 136x2​+9y2​=1 ​

Find the vertex,focus,and directrix of the parabola.​ (x−1)2+16(y+6)=0( x - 1 ) ^ { 2 } + 16 ( y + 6 ) = 0(x−1)2+16(y+6)=0 ​

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 5 inches

Find the vertex,focus,and directrix of the parabola.​ (x+3)+(y−1)2=0( x + 3 ) + ( y - 1 ) ^ { 2 } = 0(x+3)+(y−1)2=0 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Ellipses

Hyperbolas

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 9 } { 2 } x$

Give the coordinates of the circle's center and its radius. $( x - 6 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4$

Select the graph of the following equation. $x ^ { 2 } = 8 y$

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 3 } { 4 } x$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( 0 , \frac { 1 } { 2 } \right)$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±2);asymptotes: y = ± $\frac { 3 } { 2 }$ x

The revenue R (in dollars)generated by the sale of x units of a patio furniture set is given by $( x - 116 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 16,820 )$ .Approximate the number of sales that will maximize revenue.

Find the vertex,focus,and directrix of the parabola. $x ^ { 2 } + 4 y = 0$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( 0 , - 4 )$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -5

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 1 } { 7 } x$

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$

Find the vertex,focus,and directrix of the parabola. $( x - 1 ) ^ { 2 } + 16 ( y + 6 ) = 0$

Find the vertex,focus,and directrix of the parabola. $( x + 3 ) + ( y - 1 ) ^ { 2 } = 0$