Question 1

Find the vertex and focus of the parabola for the given equation and select its graph.​ $$y = - 3 x ^ { 2 }$$ ​

Accepted Answer

A) Vertex: (0,0) Focus: (0,3)   
B) Vertex: (0,0) Focus: (0,-12)   
C) Vertex: (0,0) Focus: (0,-3)   
D) Vertex: (0,0) Focus: $$\left( 0 , - \frac { 1 } { 12 } \right)$$   
E) Vertex: (0,0) Focus: $$\left( 0 , \frac { 1 } { 3 } \right)$$   
A) Vertex: (0,0) Focus: (0,3)   
B) Vertex: (0,0) Focus: (0,-12)   
C) Vertex: (0,0) Focus: (0,-3)   
D) Vertex: (0,0) Focus: $$\left( 0 , - \frac { 1 } { 12 } \right)$$   
E) Vertex: (0,0) Focus: $$\left( 0 , \frac { 1 } { 3 } \right)$$

Question 2

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -9

Accepted Answer

A) x2 = -9y 
B) y2 = 36x 
C) x2 = -36y 
D) x2 = 36y 
E) y2 = -9x 
A) x2 = -9y 
B) y2 = 36x 
C) x2 = -36y 
D) x2 = 36y 
E) y2 = -9x

Question 3

As a speeding train crosses a trestle over a deep gorge,a child drops his toy plane from the window.The path of the toy plane is modeled by $x ^ { 2 } = - 7.0 ( y - 185 )$ ,where y is the height above the floor of the gorge and distances are measured in feet.How far will the toy plane travel horizontally before it hits the bottom of the gorge? [Note: The toy plane does not glide;it "drops like a rock."]

Accepted Answer

A) 7.0 ft 
B) 36.0 ft 
C) 185 ft 
D) 1295.0 ft 
E) 14 ft 
A) 7.0 ft 
B) 36.0 ft 
C) 185 ft 
D) 1295.0 ft 
E) 14 ft

Question 4

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

Question 5

Give the standard form of the equation of the parabola with the given characteristics. vertex: (7,8)focus: (5,8)

Accepted Answer

A)  $( y + 8 ) ^ { 2 } = - 8 ( x + 7 )$ 
B)  $( y - 8 ) ^ { 2 } = - 8 ( x - 7 )$ 
C)  $( x + 7 ) ^ { 2 } = 8 ( y + 8 )$ 
D)  $( y - 8 ) ^ { 2 } = 8 ( x - 7 )$ 
E)  $( x - 7 ) ^ { 2 } = 8 ( y - 8 )$ 
A)  $( y + 8 ) ^ { 2 } = - 8 ( x + 7 )$ 
B)  $( y - 8 ) ^ { 2 } = - 8 ( x - 7 )$ 
C)  $( x + 7 ) ^ { 2 } = 8 ( y + 8 )$ 
D)  $( y - 8 ) ^ { 2 } = 8 ( x - 7 )$ 
E)  $( x - 7 ) ^ { 2 } = 8 ( y - 8 )$

Question 6

Find the vertex and focus of the parabola from the given equation and select its graph.​ $$2 x + y ^ { 2 } = 0$$ ​

Accepted Answer

A) Vertex: (0,0) Focus: (- $\frac { 1 } { 2 }$ ,0)   
B) Vertex: (- $\frac { 1 } { 2 }$ ,0) Focus: (0,0)   
C) Vertex: (0,0) Focus: (0, $\frac { 1 } { 2 }$ )   
D) Vertex: (0,0) Focus: (0,- $\frac { 1 } { 2 }$ )   
E) Vertex: (0,0) Focus: ( $\frac { 1 } { 2 }$ ,0)   
A) Vertex: (0,0) Focus: (- $\frac { 1 } { 2 }$ ,0)   
B) Vertex: (- $\frac { 1 } { 2 }$ ,0) Focus: (0,0)   
C) Vertex: (0,0) Focus: (0, $\frac { 1 } { 2 }$ )   
D) Vertex: (0,0) Focus: (0,- $\frac { 1 } { 2 }$ )   
E) Vertex: (0,0) Focus: ( $\frac { 1 } { 2 }$ ,0)

Question 7

Find the vertex and directrix of the parabola. $$x ^ { 2 } - 14 x - 8 y + 73 = 0$$

Accepted Answer

A) vertex: $$( 7,3 )$$ directrix: $$y = 5$$ 
B) vertex: $( - 7 , - 3 )$ directrix: $y = 5$ 
C) vertex: $( 7,3 )$ directrix: $y = 1$ 
D) vertex: $( - 7 , - 3 )$ directrix: $y = - 5$ 
E) vertex: $( - 7 , - 3 )$ directrix: $y = 9$ 
A) vertex: $$( 7,3 )$$ directrix: $$y = 5$$ 
B) vertex: $( - 7 , - 3 )$ directrix: $y = 5$ 
C) vertex: $( 7,3 )$ directrix: $y = 1$ 
D) vertex: $( - 7 , - 3 )$ directrix: $y = - 5$ 
E) vertex: $( - 7 , - 3 )$ directrix: $y = 9$

Question 8

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex: $( 0,2 )$ ;directrix: $y = 10$ ​

Accepted Answer

A)  $x ^ { 2 } = - 32 ( y - 10 )$ 
B)  $y ^ { 2 } = - 32 ( x - 2 )$ 
C)  $x ^ { 2 } = 32 ( y - 2 )$ 
D)  $y ^ { 2 } = 32 ( x - 2 )$ 
E)  $x ^ { 2 } = - 32 ( y - 2 )$ 
A)  $x ^ { 2 } = - 32 ( y - 10 )$ 
B)  $y ^ { 2 } = - 32 ( x - 2 )$ 
C)  $x ^ { 2 } = 32 ( y - 2 )$ 
D)  $y ^ { 2 } = 32 ( x - 2 )$ 
E)  $x ^ { 2 } = - 32 ( y - 2 )$

Question 9

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Vertices: (0,±7);focies: (0,±4)
​

Accepted Answer

A)  $$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$$ 
B)  $$\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = 1$$ 
C)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = - 1$ 
D)  $- \frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$ 
E)  $\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = - 1$ 
A)  $$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$$ 
B)  $$\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = 1$$ 
C)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = - 1$ 
D)  $- \frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$ 
E)  $\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = - 1$

Question 10

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0,-2)

Accepted Answer

A) y2 = -8x 
B) x2 = -8y 
C) x2 = -2y 
D) y2 = -2x 
E) x2 = 2y 
A) y2 = -8x 
B) x2 = -8y 
C) x2 = -2y 
D) y2 = -2x 
E) x2 = 2y

Question 11

Find the vertices and asymptotes of the hyperbola. $25 y ^ { 2 } - 4 x ^ { 2 } = 100$

Accepted Answer

A) vertices: (±2,0),asymptote: $$y = \pm \frac { 5 } { 2 } x$$ 
B) vertices: (0,±2),asymptote: $y = \pm \frac { 2 } { 5 } x$ 
C) vertices: (±2,0),asymptote: $$y = \pm \frac { 2 } { 5 } x$$ 
D) vertices: (0,±2),asymptote: $y = \pm \frac { 5 } { 2 } x$ 
E) vertices: (±2,5),asymptote: $y = \pm \frac { 2 } { 5 } x$ 
A) vertices: (±2,0),asymptote: $$y = \pm \frac { 5 } { 2 } x$$ 
B) vertices: (0,±2),asymptote: $y = \pm \frac { 2 } { 5 } x$ 
C) vertices: (±2,0),asymptote: $$y = \pm \frac { 2 } { 5 } x$$ 
D) vertices: (0,±2),asymptote: $y = \pm \frac { 5 } { 2 } x$ 
E) vertices: (±2,5),asymptote: $y = \pm \frac { 2 } { 5 } x$

Question 12

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (±3,0);passes through the point ​ $( 5 , \sqrt { 3 } )$ ​

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 27 / 16 } = - 1$ 
B)  $\frac { x ^ { 2 } } { 27 / 16 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 27 / 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 27 / 16 } + \frac { y ^ { 2 } } { 9 } = - 1$ 
E)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 27 / 16 } = 1$ 
A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 27 / 16 } = - 1$ 
B)  $\frac { x ^ { 2 } } { 27 / 16 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 27 / 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 27 / 16 } + \frac { y ^ { 2 } } { 9 } = - 1$ 
E)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 27 / 16 } = 1$

Question 13

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Directrix: $y = 3$ ​

Accepted Answer

A)  $y ^ { 2 } = - 12 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 12 x$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $x ^ { 2 } = - 12 y$ 
A)  $y ^ { 2 } = - 12 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 12 x$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $x ^ { 2 } = - 12 y$

Question 14

Find the vertex and focus of the parabola from the given equation and select its graph.​ $$y ^ { 2 } = 6 x$$ ​

Accepted Answer

A) Vertex: (0,0) Focus: (- $\frac { 3 } { 2 }$ ,0)   
B) Vertex: (0,0) Focus: (0,- $\frac { 3 } { 2 }$ )   
C) Vertex: (0,0) Focus: ( $\frac { 3 } { 2 }$ ,0)   
D) Vertex: (0,0) Focus: (0, $\frac { 3 } { 2 }$ )   
E) Vertex: (0,0) Focus: ( $\frac { 3 } { 2 }$ ,0)   
A) Vertex: (0,0) Focus: (- $\frac { 3 } { 2 }$ ,0)   
B) Vertex: (0,0) Focus: (0,- $\frac { 3 } { 2 }$ )   
C) Vertex: (0,0) Focus: ( $\frac { 3 } { 2 }$ ,0)   
D) Vertex: (0,0) Focus: (0, $\frac { 3 } { 2 }$ )   
E) Vertex: (0,0) Focus: ( $\frac { 3 } { 2 }$ ,0)

Question 15

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

Accepted Answer

A) Vertex: (0,0);Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 3 } { 4 }$ 
B) Vertex: (0,0);Focus: $\left( - \frac { 1 } { 3 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 3 }$ 
C) Vertex: (0,0);Focus: $\left( \frac { 1 } { 3 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 3 }$ 
D) Vertex: (0,0);Focus: $\left( \frac { 3 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 3 } { 4 }$ 
E) Vertex: (0,0);Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ;Directrix: $x = \frac { 3 } { 4 }$ 
A) Vertex: (0,0);Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 3 } { 4 }$ 
B) Vertex: (0,0);Focus: $\left( - \frac { 1 } { 3 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 3 }$ 
C) Vertex: (0,0);Focus: $\left( \frac { 1 } { 3 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 3 }$ 
D) Vertex: (0,0);Focus: $\left( \frac { 3 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 3 } { 4 }$ 
E) Vertex: (0,0);Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ;Directrix: $x = \frac { 3 } { 4 }$

Question 16

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance)shown in the picture.   ​ d = 2.25 inches

Accepted Answer

A)  $x ^ { 2 } = 9 y$ 
B) ​ $y ^ { 2 } = \frac { 1 } { 9 } x$ 
C) ​ $x ^ { 2 } = 2.25 y$ 
D) ​ $y ^ { 2 } = 2.25 x$ 
E)  $y ^ { 2 } = 9 x$ 
A)  $x ^ { 2 } = 9 y$ 
B) ​ $y ^ { 2 } = \frac { 1 } { 9 } x$ 
C) ​ $x ^ { 2 } = 2.25 y$ 
D) ​ $y ^ { 2 } = 2.25 x$ 
E)  $y ^ { 2 } = 9 x$

Question 17

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex: $( - 5,5 )$ ;focus: $( - 5,0 )$ ​

Accepted Answer

A)  $( x - 5 ) ^ { 2 } = 20 ( y - 5 )$ 
B)  $( x - 5 ) ^ { 2 } = - 20 ( y - 5 )$ 
C)  $( y - 5 ) ^ { 2 } = - 20 ( x - 5 )$ 
D)  $( y - 5 ) ^ { 2 } = 20 ( x - 5 )$ 
E)  $( x + 5 ) ^ { 2 } = - 20 ( y - 5 )$ 
A)  $( x - 5 ) ^ { 2 } = 20 ( y - 5 )$ 
B)  $( x - 5 ) ^ { 2 } = - 20 ( y - 5 )$ 
C)  $( y - 5 ) ^ { 2 } = - 20 ( x - 5 )$ 
D)  $( y - 5 ) ^ { 2 } = 20 ( x - 5 )$ 
E)  $( x + 5 ) ^ { 2 } = - 20 ( y - 5 )$

Question 18

Find the center and vertices which located on the major axis of the ellipse. $$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$$

Accepted Answer

A) center: (0,0)vertices: (0,-5), (0,5) 
B) center: (0,0)vertices: (-3,0), (3,0) 
C) center: (5,3)vertices: (-5,-3), (5,3) 
D) center: (0,0)vertices: (-5,0), (5,0) 
E) center: (5,0)vertices: (0,-3), (0,3) 
A) center: (0,0)vertices: (0,-5), (0,5) 
B) center: (0,0)vertices: (-3,0), (3,0) 
C) center: (5,3)vertices: (-5,-3), (5,3) 
D) center: (0,0)vertices: (-5,0), (5,0) 
E) center: (5,0)vertices: (0,-3), (0,3)

Question 19

Identify the conic.​ $4 y ^ { 2 } - 8 x = 0$ ​

Accepted Answer

A) Circle 
B) Ellipse 
C) Parabola 
D) Hyperbola 
E) Line 
A) Circle 
B) Ellipse 
C) Parabola 
D) Hyperbola 
E) Line

Question 20

Find the vertex and focus of the parabola. $x ^ { 2 } + 8 y = 0$ ​

Accepted Answer

A) vertex: (0,0)focus: (0,-2) 
B) vertex: (2,0)focus: (0,0) 
C) vertex: (0,0)focus: (-2,0) 
D) vertex: (0,0)focus: (0,2) 
E) vertex: (-2,0)focus: (0,0) 
A) vertex: (0,0)focus: (0,-2) 
B) vertex: (2,0)focus: (0,0) 
C) vertex: (0,0)focus: (-2,0) 
D) vertex: (0,0)focus: (0,2) 
E) vertex: (-2,0)focus: (0,0)

Exam 60: Introduction to Conics Parabolas

Find the vertex and focus of the parabola for the given equation and select its graph.​ y=−3x2y = - 3 x ^ { 2 }y=−3x2 ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -9

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

Give the standard form of the equation of the parabola with the given characteristics. vertex: (7,8)focus: (5,8)

Find the vertex and focus of the parabola from the given equation and select its graph.​ 2x+y2=02 x + y ^ { 2 } = 02x+y2=0 ​

Find the vertex and directrix of the parabola. x2−14x−8y+73=0x ^ { 2 } - 14 x - 8 y + 73 = 0x2−14x−8y+73=0

Find the standard form of the equation of the parabola with the given characteristics. ​ Vertex: (0,2)( 0,2 )(0,2) ;directrix: y=10y = 10y=10 ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Vertices: (0,±7);focies: (0,±4) ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0,-2)

Find the vertices and asymptotes of the hyperbola. 25y2−4x2=10025 y ^ { 2 } - 4 x ^ { 2 } = 10025y2−4x2=100

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​ Vertices: (±3,0);passes through the point ​ (5,3)( 5 , \sqrt { 3 } )(5,3​) ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Directrix: y=3y = 3y=3 ​

Find the vertex and focus of the parabola from the given equation and select its graph.​ y2=6xy ^ { 2 } = 6 xy2=6x ​

Find the vertex,focus,and directrix of the parabola.​ y2=−3xy ^ { 2 } = - 3 xy2=−3x ​

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance)shown in the picture. ​ d = 2.25 inches

Find the standard form of the equation of the parabola with the given characteristics. ​ Vertex: (−5,5)( - 5,5 )(−5,5) ;focus: (−5,0)( - 5,0 )(−5,0) ​

Find the center and vertices which located on the major axis of the ellipse. x225+y29=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 125x2​+9y2​=1

Identify the conic.​ 4y2−8x=04 y ^ { 2 } - 8 x = 04y2−8x=0 ​

Find the vertex and focus of the parabola. x2+8y=0x ^ { 2 } + 8 y = 0x2+8y=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

Find the vertex and focus of the parabola for the given equation and select its graph. $y = - 3 x ^ { 2 }$

Find the vertex and focus of the parabola from the given equation and select its graph. $2 x + y ^ { 2 } = 0$

Find the vertex and directrix of the parabola. $x ^ { 2 } - 14 x - 8 y + 73 = 0$

Find the standard form of the equation of the parabola with the given characteristics. Vertex: $( 0,2 )$ ;directrix: $y = 10$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (0,±7);focies: (0,±4)

Find the vertices and asymptotes of the hyperbola. $25 y ^ { 2 } - 4 x ^ { 2 } = 100$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±3,0);passes through the point $( 5 , \sqrt { 3 } )$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Directrix: $y = 3$

Find the vertex and focus of the parabola from the given equation and select its graph. $y ^ { 2 } = 6 x$

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

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance)shown in the picture. d = 2.25 inches

Find the standard form of the equation of the parabola with the given characteristics. Vertex: $( - 5,5 )$ ;focus: $( - 5,0 )$

Find the center and vertices which located on the major axis of the ellipse. $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$

Identify the conic. $4 y ^ { 2 } - 8 x = 0$

Find the vertex and focus of the parabola. $x ^ { 2 } + 8 y = 0$