Deck 12: Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Question 1

Graph the equation. $y = \frac { 10 } { x ^ { 2 } }$

A)
B)
C)
D)

Answer 1

Question 2

Find y if the line through (0, 2) and ( 2, y ) has a slope of $- \frac { 3 } { 2 }$

A) 5
B) -1
C) 10
D) 4

Answer 2

5

Question 3

Graph the equation. y = $-$ x 3 $-$ 3

A)
B)
C)
D)

Answer 3

Question 4

Find the distance between the points (3, -5) and (6, -1).

A) 2
B) 10
C) 8
D) 5

Question 5

Find the slope of the line determined by the points (3, 2) and (5, 6).

A) $- \frac { 1 } { 2 }$
B) $\frac { 1 } { 2 }$
C) $-$ 2
D) 2

Question 6

Graph the equation. y = x + 4

A)
B)
C)
D)

Question 7

The graph of an equation is symmetric with respect to the y axis if replacing x with $- x$ results in an equivalent equation.

Question 8

Graph the equation. y = $-$ 3 x $-$ 2

A)
B)
C)
D)

Question 9

Graph the equation. y = x 2 $-$ 2

A)
B)
C)
D)

Question 10

The distance between $P _ { 1 }$ and $P _ { 2 }$ is the same as the distance between $P _ { 2 }$ and $P _ { 1 }$ .

Question 11

If the point $( 3 , - 5 )$ is on a graph that is symmetric with respect to the x axis, the point $( - 3 , - 5 )$ is also on the graph.

Question 12

For the point (1, 8) determine the point that is symmetric with respect to y -axis.

A) (1, -8)
B) (0, 8)
C) (-1, -8)
D) (-1, 8)

Question 13

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x ² + 5 y = -6.

A) symmetry with respect to the x axis
B) symmetry with respect to the y axis
C) symmetry with respect to the origin

Question 14

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x 2 $-$ 4 x $-$ y 2 = 3.

A) symmetry with respect to the x axis
B) symmetry with respect to the origin
C) symmetry with respect to the y axis

Question 15

Find the distance between the points (14, 9) and (-1, -9).

A) $\sqrt { 183 }$
B) $3 \sqrt { 61 }$
C) $\sqrt { 61 }$
D) 61

Question 16

Find x if the line through ( 2, 2) and ( x , 7) has a slope of $\frac { 9 } { 8 }$

A) -10
B) 3
C) 6
D) 11

Question 17

The slope of a line is the ratio of the horizontal change to the vertical change when moving from one point to another point.

Question 18

Find the slope of the line determined by the points ( $-$ 4, 0) and (0, $-$ 7).

A) $\frac { 7 } { 4 }$
B) $\frac { 4 } { 7 }$
C) $- \frac { 7 } { 4 }$
D) 0

Question 19

Find the slope of the line determined by the points (2, 1) and (7, -19).

A) $-$ 4
B) $\frac { 1 } { 4 }$
C) $- \frac { 1 } { 4 }$
D) 4

Question 20

Graph the equation. 3 x $-$ y = 2

A)
B)
C)
D)

Question 21

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph.

-symmetry with respect to the x axis

A) $x ^ { 2 } + 2 y = 2$
B) $x = - y ^ { 2 } + 6$
C) $x y = 2$

Question 22

Find the distance between the points (9, 11) and (-6, -7). Express the answers in simplest radical form.

Question 23

For the point (-4, 5) determine the point that is symmetric with respect to y -axis. Enter your answer as an ordered pair in the form ( x , y ).

Question 24

Find the slope of the line determined by the points ( 7, 0) and (0, -4).

Question 25

Graph the equation. 2 y ² = x ³

A)
B)
C)
D)

Question 26

Find y if the line through (2, 3) and ( 3, y ) has a slope of

Question 27

Graph the equation. xy = 5

A)
B)
C)
D)

Question 28

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph.

-symmetry with respect to the origin

A) $x ^ { 2 } + 2 y = 2$
B) $x = - y ^ { 2 } + 6$
C) $x y = 2$

Question 29

The maximum or minimum value of a parabola is found at the vertex.

Question 30

For the equation $y = a x ^ { 2 }$ the parabola is narrower than the basic parabola if $| a | < 1$ .

Question 31

Find the slope of the line determined by the points (5, 3) and (8, 18).

Question 32

Graph the equation. $y = - x ^ { 4 }$

A)
B)
C)
D)

Question 33

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph.

-symmetry with respect to the y axis

A) $x ^ { 2 } + 2 y = 2$
B) $x = - y ^ { 2 } + 6$
C) $x y = 2$

Question 34

Find the distance between the points (-4, 2) and (5, 14).

Question 35

Graph the equation. $y = \frac { - 2 } { x ^ { 2 } + 2 }$

A)
B)
C)
D)

Question 36

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph.

-symmetry with respect to the y axis

A) $x ^ { 2 } - 3 x - y ^ { 2 } = 4$
B) $y = x ^ { 4 } - x ^ { 2 } + 3$
C) $y = 2 x$

Question 37

Find x if the line through ( 1, 1) and ( x , 0) has a slope of

Question 38

Find the slope of the line determined by the points (3, 2) and (6, -1).

Question 39

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph.

-symmetry with respect to the origin

A) $x ^ { 2 } - 3 x - y ^ { 2 } = 4$
B) $y = x ^ { 4 } - x ^ { 2 } + 3$
C) $y = 2 x$

Question 40

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph.

-symmetry with respect to the x axis

A) $x ^ { 2 } - 3 x - y ^ { 2 } = 4$
B) $y = x ^ { 4 } - x ^ { 2 } + 3$
C) $y = 2 x$

Question 41

Graph the parabola. $y = ( x - 4 ) ^ { 2 } + 3$

A)
B)
C)

Question 42

Graph the parabola. $y = - \frac { 1 } { 2 } x ^ { 2 }$

A)
B)
C)

Question 43

Graph the parabola. $y = ( x + 1 ) ^ { 2 } - 3$

A)
B)
C)

Question 44

The graph of $y = ( x - 6 ) ^ { 2 } - 4$ is a parabola with the vertex at $( 6,4 )$ .

Question 45

Graph the parabola. $y = ( x - 3 ) ^ { 2 } - 4$

A)
B)
C)

Question 46

Graph the parabola. $y = ( x + 2 ) ^ { 2 }$

A)
B)
C)

Question 47

Graph the parabola. $y = ( x + 1 ) ^ { 2 } + 6$

A)
B)
C)

Question 48

Graph the parabola. $y = \frac { 1 } { 3 } x ^ { 2 } - 4$

A)
B)
C)

Question 49

Graph the parabola. $y = 4 x ^ { 2 } + 3$

A)
B)
C)

Question 50

Graph the parabola. $y = ( x - 4 ) ^ { 2 }$

A)
B)
C)

Question 51

Graph the parabola. $y = x ^ { 2 } + 7$

A)
B)
C)

Question 52

Graph the parabola. $y = - 2 x ^ { 2 } - 5$

A)
B)
C)

Question 53

Graph the parabola. $y = 2 x ^ { 2 }$

A)
B)
C)

Question 54

Graph the parabola. $y = - 5 x ^ { 2 }$

A)
B)
C)

Question 55

Graph the parabola. $y = \frac { 1 } { 5 } x ^ { 2 }$

A)
B)
C)

Question 56

Graph the parabola. $y = x ^ { 2 } - 1$

A)
B)
C)

Question 57

Graph the parabola. $y = 4 ( x - 1 ) ^ { 2 } - 2$

A)
B)
C)

Question 58

Graph the parabola. $y = 3 ( x + 1 ) ^ { 2 } - 7$

A)
B)
C)

Question 59

For the equation $y = - 2 ( x + 1 ) + 2$ , the line of symmetry has x values of $- 1$ .

Question 60

Graph the parabola. $y = - ( x - 2 ) ^ { 2 } + 7$

A)
B)
C)

Question 61

Find the x intercepts of $y = x ^ { 2 } + 8 x - 3$ . Separate answers with a comma.

A) $- 4 + \sqrt { 19 }$ , $\sqrt { 19 } + 4$
B) $4 - \sqrt { 19 }$ , $\sqrt { 19 } - 4$
C) no x intercepts
D) $- 4 - \sqrt { 19 }$ , $\sqrt { 19 } - 4$

Question 62

Graph the parabola. $y = - 2 ( x - 2 ) ^ { 2 } - 3$

A)
B)
C)

Question 63

Identify the graph of the parabola. y = $-$ x 2 $-$ 4 x $-$ 3

A)
B)
C)
D)

Question 64

The equation $y = 4 x ^ { 2 } + 2 x - 5$ will have the exact same shape as the graph $y = \frac { 1 } { 4 } ( x - 3 ) ^ { 2 } - 5$ .

Question 65

Find the length of a radius of this circle. x ² + y ² = 41

A) $r = \sqrt { 41 }$
B) $r = 1$
C) $r = 41$
D) $r = \sqrt { 2 }$

Question 66

Find the x intercepts of $y = 3 x ^ { 2 } + 6 x + 7$ . Separate answers with a comma.

A) $\frac { 3 + 2 \sqrt { 3 } } { 2 }$ , $\frac { 3 - 2 \sqrt { 3 } } { 2 }$
B) $\frac { - 3 + 2 \sqrt { 3 } } { 2 }$ , $\frac { - 3 - 2 \sqrt { 3 } } { 2 }$
C) 7
D) no x intercepts

Question 67

Graph the parabola. $y = - \frac { 1 } { 3 } ( x + 4 ) ^ { 2 } - 2$

A)
B)
C)

Question 68

A line segment determined by the center and any point on the circle is called a diameter.

Question 69

Graph the circle. $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 9$

A)
B)
C)
D)
E)

Question 70

For the circle $( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 9$ , the vertex is $( 2 , - 1 )$ .

Question 71

Identify the graph of the parabola. y = $-$ 4 x 2 + 40 x $-$ 57

A)
B)
C)
D)

Question 72

Identify the graph of the parabola. y = x ² + 13 x + 14

A)
B)
C)
D)

Question 73

Find the length of a radius of the circle. 64 x 2 + 64 y 2 $-$ 16 x $-$ 112 y $-$ 2,446 = 0

A) $r = 1,521$
B) $r = 1$
C) $r = \sqrt { 39 }$
D) $r = 3 \sqrt { 39 }$
E) $r = 39$

Question 74

Graph the circle. $x ^ { 2 } + y ^ { 2 } = 25$

A)
B)
C)
D)
E)

Question 75

Identify the graph of the parabola. y = 2 x ² + 8 x + 13

A)
B)
C)
D)

Question 76

Graph the circle. $x ^ { 2 } + y ^ { 2 } - 6 x - 6 y - 18 = 0$

A)
B)
C)
D)
E)

Question 77

Identify the graph of the parabola. y = x 2 $-$ 8 x + 21

A)
B)
C)
D)

Question 78

Identify the graph of the parabola. y = x ² + 10 x + 21

A)
B)
C)
D)

Question 79

Find the x intercepts of $y = 3 x ^ { 2 } - 11 x - 4$ . Separate answers with a comma.

A) no x intercepts
B) $- \frac { 1 } { 3 }$ , $- 4$
C) $- \frac { 1 } { 3 }$ , 4
D) $\frac { 1 } { 3 }$ , 4

Question 80

The general approach of changing $y = a x ^ { 2 } + b x + c$ to $y = a ( x - h ) ^ { 2 } + k$ is by completing the square.