Quiz about Quadratics Review

Question 1

Convert to vertex form.

Accepted Answer

y=3(x+1)² - 8

Answer

y=3(x-1)² - 8

Answer

y=3(x+2)² - 8

Answer

y=3(x-2)² - 8

Question 2

If the blue is f(x)=x^2,the red must be

Accepted Answer

g(x)=(x-3)²

Answer

g(x)=(x+3)²

Answer

g(x)=x2+3

Answer

g(x)=x2-2

Question 3

Write the quadratic equation in standard form for a parabola with a vertex at $$(2, -3)$$ and passing through the point $$(3, 2)$$ .

Accepted Answer

$$y = x^2 - 4x + 7$$

Answer

$$y = x^2 - 4x + 1$$

Answer

$$y = x^2 - 4x + 5$$

Answer

$$y = x^2 - 4x - 3$$

Question 4

Identify the vertex of the quadratic function $$f(x) = 2(x - 1)^2 + 3$$ .

Accepted Answer

$$(1, 3)$$

Answer

$$(-1, 3)$$

Answer

$$(1, -3)$$

Answer

$$(-1, -3)$$

Question 5

Transform the quadratic function $$f(x) = x^2$$ by shifting it 4 units to the right and 2 units up. What is the new function?

Accepted Answer

$$f(x) = (x - 4)^2 + 2$$

Answer

$$f(x) = (x + 4)^2 + 2$$

Answer

$$f(x) = (x - 4)^2 - 2$$

Answer

$$f(x) = (x + 4)^2 - 2$$

Question 6

Convert the quadratic function $$f(x) = x^2 + 6x + 8$$ to vertex form.

Accepted Answer

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

Answer

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

Answer

$$f(x) = (x + 3)^2 + 1$$

Answer

$$f(x) = (x - 3)^2 - 1$$

Question 7

Write the quadratic equation in vertex form for a parabola with a vertex at $$(-2, 5)$$ and passing through the point $$(0, 1)$$ .

Accepted Answer

$$y = -1(x + 2)^2 + 5$$

Answer

$$y = 2(x + 2)^2 + 5$$

Answer

$$y = -1(x - 2)^2 + 5$$

Answer

$$y = 2(x - 2)^2 + 5$$

Question 8

Identify the vertex of the quadratic function $$f(x) = -3(x + 4)^2 + 7$$ .

Accepted Answer

$$(-4, 7)$$

Answer

$$(4, 7)$$

Answer

$$(-4, -7)$$

Answer

$$(4, -7)$$

Question 9

Transform the quadratic function $$f(x) = x^2$$ by reflecting it over the x-axis and shifting it 3 units down. What is the new function?

Accepted Answer

$$f(x) = -x^2 - 3$$

Answer

$$f(x) = x^2 - 3$$

Answer

$$f(x) = -x^2 + 3$$

Answer

$$f(x) = x^2 + 3$$

Question 10

Convert the quadratic function $$f(x) = 3x^2 - 12x + 7$$ to vertex form.

Accepted Answer

$$f(x) = 3(x - 2)^2 - 5$$

Answer

$$f(x) = 3(x + 2)^2 + 5$$

Answer

$$f(x) = 3(x - 2)^2 + 5$$

Answer

$$f(x) = 3(x + 2)^2 - 5$$

Question 11

Write the quadratic equation in standard form for a parabola with a vertex at $$(0, 0)$$ and passing through the point $$(2, 8)$$ .

Accepted Answer

$$y = 4x^2$$

Answer

$$y = 2x^2$$

Answer

$$y = 8x^2$$

Answer

$$y = x^2$$

Question 12

Identify the vertex of the quadratic function $$f(x) = \frac{1}{2}(x - 5)^2 - 4$$ .

Accepted Answer

$$(5, -4)$$

Answer

$$(-5, -4)$$

Answer

$$(5, 4)$$

Answer

$$(-5, 4)$$

Question 13

Transform the quadratic function $$f(x) = x^2$$ by stretching it vertically by a factor of 3 and shifting it 1 unit to the left. What is the new function?

Accepted Answer

$$f(x) = 3(x + 1)^2$$

Answer

$$f(x) = 3(x - 1)^2$$

Answer

$$f(x) = \frac{1}{3}(x + 1)^2$$

Answer

$$f(x) = \frac{1}{3}(x - 1)^2$$

Question 14

Convert the quadratic function $$f(x) = x^2 - 4x + 6$$ to vertex form.

Accepted Answer

$$f(x) = (x - 2)^2 - 2$$

Answer

$$f(x) = (x - 2)^2 + 2$$

Answer

$$f(x) = (x + 2)^2 - 2$$

Answer

$$f(x) = (x + 2)^2 + 2$$

Question 15

Write the quadratic equation in vertex form for a parabola with a vertex at $$(3, -2)$$ and passing through the point $$(5, 6)$$ .

Accepted Answer

$$y = 2(x - 3)^2 - 2$$

Answer

$$y = 4(x - 3)^2 - 2$$

Answer

$$y = 2(x + 3)^2 - 2$$

Answer

$$y = 4(x + 3)^2 - 2$$

Question 16

Which of the following equations is written in the standard form for quadratic equations?

Accepted Answer

y = 4x² - 7x + 11

Answer

8x + 4y = 12

Answer

3x² + 2x = 1

Answer

2x² - x³ + 14 = y

Question 17

Which of the following graphs appropriately marks the axis of symmetry?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 18

Does the graph of $$y=-3x^2-2x+9$$ have a MINIMUM or a MAXIMUM?

Accepted Answer

MAXIMUM

Answer

MINIMUM

Answer

CANNOT BE DETERMINED

Question 19

Does the graph of $$y=4x^2-7x-3$$ have a MINIMUM or a MAXIMUM? Why?

Accepted Answer

MINIMUM, because the value of "a" is positive.

Answer

MAXIMUM, because "a" times "c" is -12.

Answer

CANNOT BE DETERMINED

Question 20

What are the other names for the "solution(s)" to a quadratic equation?

**Select all that apply!**

Accepted Answer

root(s)

Accepted Answer

x-intercept(s)

Accepted Answer

zero(s)

Answer

y-intercept(s)

Question 21

Describe the transformations from

f(x) = x²

to

g(x) = -0.3x² + 4

Accepted Answer

reflection over x-axis, vertical compression, and shift up

Answer

vertical compression and shift up

Answer

reflection over x-axis, vertical stretch, and shift up

Answer

vertical stretch and shift down

Question 22

Which graph will be the most vertically stretched compared to the quadratic parent function?

Accepted Answer

g(x) = 5x² + 1

Answer

g(x) = -x² + 9

Answer

g(x) = 0.2x² - 11

Answer

g(x) = -3x² - 6

Question 23

Select the answer that has a, b, and c correctly labeled:

$$y=-x^2+2x-9$$

Accepted Answer

a= -1, b= 2, c= -9

Answer

a= 1, b= 2, c= -9

Answer

a= 2, b= -1, c= 9

Answer

a= -9, b= 2, c= -1

Question 24

What are the x- intercepts?

Accepted Answer

x= 0 and x= 4

Answer

x= 0 and x= -4

Answer

y= 0

Answer

x= 2

Question 25

Describe the transformations occurring to f(x) = x² + 5 if the

new equation after the transformations is

g(x) = (x - 3)² - 2

Accepted Answer

Shifted right 3 units, shifted down 7 units

Answer

Shifted left 3 units, shifted down 7 units

Answer

Shifted right 3 units, shifted up 7 units

Answer

Shifted left 3 units, shifted up 2 units

Answer

Shifted right 3 units, shifted down 2 units

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