Parabola

​9.3 The Parabola

Multiple Choice

The focus is always inside the parabola. #1

• true

• false

Multiple Choice

All parabolas with a vertical directrix open the left or right. #2

• true

• false

Multiple Choice

True or False?

When x is squared, the parabola opens up or down. #3

• True

• False

Multiple Choice

The vertex is halfway between the focus and directrix. #11

• true

• false

Multiple Choice

All parabolas with a vertical directrix open the left or right. #12

• true

• false

Multiple Choice

Find the focus of the parabola whose vertex is at the origin and whose directrix is x = 5. #23

• (5,0)

• (-5,0)

• (0,2)

• (0,-2)

Multiple Choice

What is the standard equation of a parabola that opens right and whose vertex is at the origin? #38

• $$x^2=4cy$$

• $$x^2=-4cy$$

• $$y^2=4cx$$

• $$y^2=-4cx$$

Multiple Choice

What is the standard form of the equation of the parabola with Focus: (0, 7) and the vertex at the origin? #41

• $$x^2=28y$$

• $$x^2=7y$$

• $$y^2=28x$$

• $$y^2=28x$$

Multiple Choice

What is the standard equation of a parabola that opens down and whose vertex is at $$\left(h,\ k\right)$$ ? #16

• $$\left(x-h\right)^2=4p\left(y-k\right)$$  

• $$\left(x-h\right)^2=-4p\left(y-k\right)$$

• $$\left(y-k\right)^2=4p\left(x-h\right)$$  

• $$\left(y-k\right)^2=-4p\left(x-h\right)$$

Multiple Choice

The focus is at (2,0) and the vertex is at (-4,0).  What is the equation of the parabola? #6

• y² = 24(x+4)

• (y+4)² = -12x

• x² = 16(y+4)

• (x+4)²  = -20y

Multiple Choice

(x+3)² = 4(y+5) What is the equation of the directrix? #5

• x = 4

• x = 2

• y = -4

• y = -6

Multiple Choice

(y-4)² = -8(x+1) What are the coordinates for the focus? #4

• (1,4)

• (-1,6)

• (-1,2)

• (-3,4)

Multiple Choice

What is the focus of the following parabola? (y + 5)² = -12 (x - 2) #7

• (2, - 5)

• ( -5, 2)

• (1 , -5 )

• (-1, -5 )

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Multiple Choice

Which direction does this parabola open? #8

• Up

• Down

• Left

• Right

Multiple Choice

Given the graph below, what is the equation of the parabola? #18

• $$(x+2)^2=4(y-4)$$

• $$(x+2)^2=(y-4)$$

• $$(x-2)^2=4(y+4)$$

• $$(x-2)^2=(y-4)$$

Multiple Choice

Given the graph below, what is the equation of the parabola? #19

• $$(y-4)^2=12(x+2)$$

• $$(y-4)^2=-12(x-2)$$

• $$(y+4)^2=-12(x-2)$$

• $$(y+4)^2=12(x-2)$$

Multiple Choice

Given this directrix and vertex, what would the equation of the parabola be? #20

• $$\left(y-2\right)^2=6\left(x-1\right)$$  

• $$\left(x-1\right)^2=6\left(y-2\right)$$  

• $$\left(y+2\right)^2=6\left(x+1\right)$$  

• $$\left(y-2\right)^2=-6\left(x-1\right)$$  

Multiple Choice

What is the standard form of the equation of a parabola that has a focus of $$\left(4,\ 5\right)$$  and a directrix of $$y=1$$ ? #22

• $$(x+4)^2=8(y+3)$$

• $$(x-4)^2=8(y+3)$$

• $$(x-4)^2=8(y-3)$$

• $$(x+4)^2=8(y-3)$$