Quiz about Vertex Form Review

Question 1

What is the equation of this graph?

Accepted Answer

f(x) = (x - 1)² - 5

Answer

f(x) = (x -5)² + 1

Answer

f(x) = (x + 1)² - 5

Answer

f(x) = (x + 5)² +1

Question 2

What is the vertex of the parabola given by the equation $$y = 3(x - 2)^2 + 4$$ ?

Accepted Answer

$$(2, 4)$$

Answer

$$(3, 2)$$

Answer

$$(-2, -4)$$

Answer

$$(4, 3)$$

Question 3

What is the axis of symmetry for the parabola $$y = -\frac{1}{2}(x + 5)^2 + 3$$ ?

Accepted Answer

$$x = -5$$

Answer

$$x = 5$$

Answer

$$y = 3$$

Answer

$$y = -\frac{1}{2}$$

Question 4

For the quadratic function $$y = 4(x - 1)^2 - 7$$ , what is the maximum or minimum value?

Accepted Answer

Minimum value of -7

Answer

Maximum value of 7

Answer

Maximum value of -7

Answer

Minimum value of 7

Question 5

In the vertex form of a quadratic function $$y = a(x - h)^2 + k$$ , what does the value of $$a$$ determine?

Accepted Answer

The direction of the parabola opening

Answer

The vertex of the parabola

Answer

The axis of symmetry

Answer

The y-intercept

Question 6

Given the quadratic function in vertex form $$y=-(x+3)^2+5$$ , identify the transformation from the parent function $$y = x^2$$ .

Accepted Answer

Shift left 3 units, up 5 units, open down

Answer

Shift right 3 units, up 5 units, open down

Answer

Shift left 3 units, up 5 units, open up

Answer

Shift right 3 units, up 5 units, open up

Question 7

What is the y-intercept of the parabola given by the equation $$y = (x - 4)^2 + 2$$ ?

Accepted Answer

$$(0, 18)$$

Answer

$$(0, 2)$$

Answer

$$(0, -14)$$

Answer

$$(0, 14)$$

Question 8

How does the value of $$k$$ in the vertex form $$y = a(x - h)^2 + k$$ affect the graph of a quadratic function?

Accepted Answer

It shifts the parabola up and down.

Answer

It determines the direction in which the parabola opens.

Answer

It shifts the parabola left and right.

Answer

It affects the width of the parabola.

Question 9

Given the equation $$y = -5(x + 1)^2 - 3$$ , what is the vertex of the parabola?

Accepted Answer

$$(-1, -3)$$

Answer

$$(1, 3)$$

Answer

$$(-1, 3)$$

Answer

$$(1, -3)$$

Question 10

What is the axis of symmetry for the parabola given by $$y = 2(x - 3)^2 + 7$$ ?

Accepted Answer

$$x = 3$$

Answer

$$x = -3$$

Answer

$$y = 7$$

Answer

$$y = 2$$

Question 11

For the quadratic function $$y = -3(x + 2)^2 + 6$$ , what is the maximum or minimum value?

Accepted Answer

Maximum value of 6

Answer

Minimum value of 6

Answer

Maximum value of -6

Answer

Minimum value of -6

Question 12

In the vertex form of a quadratic function $$y = a(x - h)^2 + k$$ , what does the value of $$h$$ determine?

Accepted Answer

The axis of symmetry

Answer

The direction of the parabola opening

Answer

Shift up/down

Answer

The y-intercept

Question 13

What is the y-intercept of the parabola given by the equation $$y = -2(x - 3)^2 + 5$$ ?

Accepted Answer

$$(0,-13)$$

Answer

$$(0, 5)$$

Answer

$$(0, 23)$$

Answer

$$(0, -23)$$

Question 14

Given the equation $$y = (x - 5)^2 - 8$$ , what is the vertex of the parabola?

Accepted Answer

$$(5, -8)$$

Answer

$$(-5, 8)$$

Answer

$$(8, -5)$$

Answer

$$(-8, 5)$$

Question 15

What is the axis of symmetry for the parabola given by $$y = -\frac{1}{3}(x + 4)^2 + 2$$ ?

Accepted Answer

$$x = -4$$

Answer

$$x = 4$$

Answer

$$y = 2$$

Answer

$$y = -\frac{1}{3}$$

Question 16

For the quadratic function $$y = 5(x - 1)^2 - 9$$ , what is the maximum or minimum value?

Accepted Answer

Minimum value of -9

Answer

Maximum value of -9

Answer

Maximum value of 9

Answer

Minimum value of 9

Question 17

What is the y-intercept of the parabola given by the equation $$y=3(x-1)^2-4$$ ?

Accepted Answer

$$(0, -1)$$

Answer

$$(0, 3)$$

Answer

$$(0, -4)$$

Answer

$$(0, -7)$$

Question 18

Determine the vertex of the parabola:
y = 5x²- 20x + 13

Accepted Answer

(2, -7)

Answer

(5, -7)

Answer

(-2, -7)

Answer

(-7, -2)

Question 19

In what direction will the parabola open?
y = -3x² +7x - 2

Accepted Answer

down

Answer

up

Answer

left

Answer

right

Question 20

How do you know if a parabola has a minimum?

Accepted Answer

When "a" is positive there is a minimum

Answer

When "a" is negative there is a minimum

Answer

When all the numbers in the equation are negative there is a minimum

Answer

When all the numbers in the equation are positive there is a minimum

Question 21

How can you tell whether a parabola opens up or down by looking at the equation?

Accepted Answer

The value of "a" tells you the direction of the opening

Answer

The vertex tells you the direction of the opening

Answer

All parabolas open upward

Answer

All parabolas open downward

Question 22

A negative quadratic will open.....

Accepted Answer

downward

Answer

upward

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