Free Printable Conics

1.

The focus is always inside the parabola.

a)

true

b)

false

2.

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

a)

true

b)

false

3.

True or False?
When the x-part is squared, the parabola opens up or down.

a)

True

b)

False

4.

What are the coordinates for the focus? $x+1=-\frac{1}{8}\left(y-4\right)^2$

a)

$\left(1,4\right)$

b)

$\left(-1,6\right)$

c)

$\left(-1,2\right)$

d)

$\left(-3,4\right)$

5.

What is the equation of the directrix? $x+5=\frac{1}{4}\left(y+3\right)^2$

a)

$y=4$

b)

$x=2$

c)

$y=-4$

d)

$x=-6$

6.

Which direction does this parabola open?
$x-2=-\frac{1}{4}\left(y+1\right)^2$

a)

Up

b)

Down

c)

Left

d)

Right

7.

Which equation below represents a parabola that opens upward with a vertex at $\left(0,-5\right)$ ?

a)

$y-5=x^2$

b)

$y+5=x^2$

c)

$y=\left(x-5\right)^2$

d)

$y=\left(x+5\right)^2$

8.

What is the green dashed line called?

a)

directrix

b)

parabola

c)

axis of symmetry

d)

asymptote

9.

What is the axis of symmetry for a parabola that opens right with a vertex at $\left(-3,2\right)$ .

a)

$y=-2$

b)

$x=3$

c)

$x=-3$

d)

$y=2$

10.

What is the equation of the directrix? $y+5=\frac{1}{4}\left(x+3\right)^2$

a)

$x=4$

b)

$x=2$

c)

$y=-4$

d)

$y=-6$

11.

What is the "p-value" in the equation?
$x+4=-\frac{1}{40}\left(y-9\right)^2$

a)

$-10$

b)

$10$

c)

$-40$

d)

$40$

12.

What is the coordinate of the vertex?
$x+1=-\frac{1}{8}\left(y-4\right)^2$

a)

$\left(1,4\right)$

b)

$\left(-1,-4\right)$

c)

$\left(1,-4\right)$

d)

$\left(-1,4\right)$

13.

What is the coordinate of the vertex?
$y+5=\frac{1}{4}\left(x+3\right)^2$

a)

$\left(3,5\right)$

b)

$\left(-3,-5\right)$

c)

$\left(5,3\right)$

d)

$\left(-5,-3\right)$

14.

What is the value of p?
$x-6=\frac{1}{12}y^2$

a)

$12$

b)

$48$

c)

$4$

d)

$3$

15.

Given this directrix and vertex, which way would the parabola open?

a)

left

b)

right

c)

up

d)

down

16.

Where is the axis of symmetry for this parabola?

a)

$x=-1$

b)

$x=0$

c)

$y=3$

d)

$x=-3$

17.

If the directrix is $y=4$ and the focus is at
$\left(3,0\right)$ , the vertex is:

a)

$\left(3,4\right)$

b)

$\left(3,2\right)$

c)

$\left(3.5,\ 0\right)$

d)

$\left(0,\ 3.5\right)$

18.

True or False?

When the y-part is squared, the parabola opens up or down.

a)

True

b)

False

19.

This is a ___________ parabola that opens _________.

$y-11=\frac{1}{40}\left(x-5\right)^2$

a)

vertical: up

b)

vertical: down

c)

horizontal: to the right

d)

horizontal: to the left

20.

What is the domain and range of the given parabola?
$y+1=6\left(x-4\right)^2$

a)

Domain: All Real Numbers
Range: $y\ge-1$

b)

Domain: $x\ge-1$
Range: All Real Numbers

c)

Domain: All Real Numbers
Range: $y\le4$

d)

Domain: $x\ge4$
Range: All Real Numbers

21.

What is the point inside the parabola 'p' units from the vertex?

a)

vertex

b)

focus

c)

directrix

d)

axis of symmetry

22.

What is the axis of symmetry for a parabola that has a vertex at $\left(-3,2\right)$ and a focus at $\left(-3,-1\right)$

a)

$y=-2$

b)

$x=3$

c)

$x=-3$

d)

$y=2$

23.

Convert to vertex form.
$y=-2x^2+24x+5$

a)

$y+6=-2\left(x+12\right)^2$

b)

$y+31=-2\left(x-12\right)^2$

c)

$y+77=-2\left(x-6\right)^2$

d)

$y+31=-2\left(x-6\right)^2$

24.

Convert the equation to vertex form.
$y^2+x+4y+1=0$

a)

$x+3=-\left(y-2\right)^2$

b)

$x-3=\left(y+2\right)^2$

c)

$x-3=-\left(y+2\right)^2$

d)

none of these

25.

Bonus time!
If the focus is at $\left(2,0\right)$ and the directrix is at $x=-10$ what is the equation of the parabola?

a)

$\left(x+4\right)=\frac{1}{24}y^2$

b)

$x=-\frac{1}{12}\left(y+4\right)^2$

c)

$y+4=\frac{1}{16}x^2$

d)

$y=-\frac{1}{20}\left(x+4\right)^2$

Conics - Parabolas

Total questions: 25

Worksheet time: 47mins

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