Free Printable Vertex form of a quadratic

1.

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (-1,4); point (1,0)

f\left(x\right)=a\left(x-h\right)^2+k

a)

$f\left(x\right)=-\left(x+1\right)^2+4$

b)

$f\left(x\right)=\left(x+1\right)^2+4$

c)

$f\left(x\right)=-\left(x+4\right)^2+1$

d)

$f\left(x\right)=-\left(x+1\right)^2$

2.

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (-2,-1); point (0,3)

f\left(x\right)=a\left(x-h\right)^2+k

a)

$f\left(x\right)=-\left(x+1\right)^2+3$

b)

$f\left(x\right)=\left(x+2\right)^2-1$

c)

$f\left(x\right)=-\left(x+5\right)^2+7$

d)

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

3.

What steps transform the graph y = x² to y = x² + 8

a)

shifted up 8 units

b)

shifted down 8 units

c)

shifted left 8 units

d)

shifted right 8 units

4.

What steps transform the graph y = x² to y = (x-4)²

a)

Shifted down 4 units

b)

Shifted left 4 units

c)

Shifted right 4 units

d)

Shifted up 4 units

5.

Given

f\left(x\right)=\left(x-3\right)^2+5

, what transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Left 3 and down 5

c)

Right 3 and down 5

d)

Right 3 and up 5

6.

Which equation describes the transformation of shifting

f\left(x\right)=x^2

two units right?

a)

$x^2+2$

b)

$\left(x+2\right)^2$

c)

$x^2-2$

d)

$\left(x-2\right)^2$

7.

Find the equation of the parabola that has moved...

5 units to the right

a)

y=x^2+5

b)

$y=x^2-5$

c)

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

d)

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

8.

Which of the following is the correct equation for the given graph?

a)

f(x) = -(x + 2)² - 4

b)

f(x) = -(x - 2)² - 4

c)

f(x) = -3(x - 2)² - 4

d)

f(x) = -3(x + 2)² - 4

9.

Which quadratic function is represented by the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

10.

a)

y = -(x + 1)² - 4

b)

y = -(x + 1)² + 4

c)

y = -(x - 1)² - 4

d)

y = (x + 1)² + 4

11.

a)

y = (x - 2)² + 2

b)

y = (x + 2)² + 2

c)

y = (x - 2)² - 2

d)

y = -(x - 2)² + 2

12.

If path of a projectile is modeled by:
h(t) = -16t² + 20t +6, what is the height after 1 second?

a)

6 feet

b)

20 feet

c)

10 feet

d)

4 feet

13.

What direction is the following equation opening?
y=-3x²-7x+8

a)

Up

b)

Down

c)

Left

d)

Right

14.

What is the vertex for
f(x)=4(x-2)² + 3

a)

(-2, 3)

b)

(2,-3)

c)

(4,3)

d)

(2,3)

15.

$f\left(x\right)=-\left(x-4\right)^2+1$

Choose the correct graph of the equation.

a)

b)

c)

d)

16.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

17.

Which equation matches the graph?

a)

$f\left(x\right)=\left(x-1\right)^2+4$

b)

$f\left(x\right)=\left(x+4\right)^2-1$

c)

$f\left(x\right)=-\left(x-1\right)^2+4$

d)

$f\left(x\right)=-\left(x+4\right)^2-1$

18.

Describe the horizontal shift for

y = 3(x + 4)² - 1

a)

shifts 3 left

b)

shifts 4 left

c)

shifts 4 right

d)

shifts 1 left

19.

What happens to the parabola when you multiply its equation by a number bigger than 1? Eg y = 3x²

a)

Graph moves UP

b)

Graph gets WIDER

c)

Graph moves DOWN

d)

Graph gets NARROWER

20.

Which quadratic function is represented by the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

21.

Find the y-intercept of the function

y = -3(x + 2)² - 5

a)

(0, -5)

b)

(-2, -5)

c)

(0, -17)

d)

(2, -5)

22.

What causes the graph of y = x² to open downward?

a)

multiply the x² by a fraction

b)

multiply the x² by a decimal

c)

multiply the x² by a negative number

d)

multiply the x² by a number greater than 1

23.

A cable is attached at the same height from two poles and hangs between them such that its height above the

ground, y, in inches, can be modelled using the equation: $y=x^2-16x+67$

where x represents the horizontal distance from the left

pole, in feet.

What height is point B above the ground? Leave out the unit in the answer.

(a)

24.

A cable is attached at the same height from two poles and hangs between them such that its height above the

ground, y, in inches, can be modelled using the equation: $y=x^2-16x+67$

where x represents the horizontal distance from the left

pole, in feet.

What is the difference in the heights of points

A and B? Leave out the unit in the answer.

(a)

25.

A cable is attached at the same height from two poles and hangs between them such that its height above the

ground, y, in inches, can be modelled using the equation: $y=x^2-16x+67$

where x represents the horizontal distance from the left

pole, in feet.

What is the horizontal distance that separates

points A and C? Leave out the unit in the answer.

(a)

Vertex form of a quadratic

Total questions: 25

Worksheet time: 31mins

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