Quiz about Transformations and Characteristics of Quadratics

Question 1

Which of the following describes the graph of the function $$f(x)=\left(x-2\right)^2$$ ?

Accepted Answer

A U-shaped graph with vertex at (2, 0)

Answer

A V-shaped graph with vertex at (2, 0)

Answer

A V-shaped graph with vertex at (-2, 0)

Answer

A U-shaped graph with vertex at (-2, 0)

Question 2

Which of the following represents a vertical translation of the quadratic function $$f(x) = x^2$$ by 3 units up?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 3

What is the name of the curved graph of a quadratic function?

Accepted Answer

Parabola

Answer

Happy face

Answer

Hyperbole

Answer

The letter "U"

Question 4

Identify the transformation of the quadratic function $$f(x) = x^2$$ to $$g(x) = (x - 4)^2 + 2$$ .

Accepted Answer

Shifted 4 units right and 2 units up

Answer

Shifted 4 units left and 2 units up

Answer

Shifted 4 units left and 2 units down

Answer

Shifted 4 units right and 2 units down

Question 5

What is the effect on the graph of the function $$f(x)=x^2$$ when it is transformed to $$g(x)=-x^2$$ ?

Accepted Answer

Reflection across the x-axis

Answer

Reflection across the y-axis

Answer

Vertical shift up

Answer

Vertical shift down

Question 6

What is the vertex of the quadratic function $$f(x) = (x + 1)^2 - 4$$ ?

Accepted Answer

(-1, -4)

Answer

(1, -4)

Answer

(-1, 4)

Answer

(1, 4)

Question 7

Which of the following transformations applies to the function $$f(x) = x^2$$ to get $$g(x) = -x^2 + 3$$ ?

Accepted Answer

Reflection across the x-axis and shift up 3 units

Answer

Reflection across the y-axis and shift up 3 units

Answer

Reflection across the y-axis and shift down 3 units

Answer

Reflection across the x-axis and shift down 3 units

Question 8

Given the function $$f(x)=-2x^2+4x-7$$ , what is the value of $$a$$ ?

Accepted Answer

-2

Answer

2

Answer

4

Answer

-7

Question 9

What is the axis of symmetry of the quadratic function $$f(x) = (x + 1)^2 - 4$$ ?

Accepted Answer

x = -1

Answer

x = 1

Answer

y = -1

Answer

y = -4

Question 10

Which of the following represents a vertical stretch of the quadratic function $$f(x) = x^2$$ by a factor of 3?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 11

Identify the transformation of the absolute value function $$f(x)=x^2$$ to $$g(x)=\left(x+5\right)^2-2$$ .

Accepted Answer

Shifted 5 units left and 2 units down

Answer

Shifted 5 units left and 2 units up

Answer

Shifted 5 units right and 2 units up

Answer

Shifted 5 units right and 2 units down

Question 12

What is the y-intercept of the quadratic function $$f(x)=4x^2+2x-3$$ ?

Accepted Answer

-3

Answer

2

Answer

3

Answer

4

Question 13

What does a vertical translation do to the graph of a function?

Accepted Answer

Moves it up or down

Answer

Flips it over the x-axis

Answer

Moves it left or right

Answer

Stretches it along the -axis

Question 14

Identify the axis of symmetry for the graph shown.

Accepted Answer

x = 3

Answer

x = -3

Answer

y = -4

Answer

y = 3

Question 15

Which of the following represents a horizontal compression of the quadratic function $$f(x) = x^2$$ by a factor of $$\frac{1}{2}$$ ?

Accepted Answer

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

Answer

$$f(x) = \left(\frac{1}{2}x\right)^2$$

Answer

$$f(x) = \left(\frac{1}{2}x^2\right)$$

Answer

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

Question 16

What is the effect on the graph of the function $$f(x) = x^2$$ when it is transformed to $$g(x) = (x - 3)^2$$ ?

Accepted Answer

Shifted 3 units right

Answer

Shifted 3 units left

Answer

Shifted 3 units up

Answer

Shifted 3 units down

Question 17

If a quadratic function has x intercepts at (2, 0 ) and (6, 0), what is the axis of symmetry?

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 0

Answer

x = 6

Question 18

.
Blue is the parent function f(x)=x²

Red is another function g(x).

What could be the equation of the RED function.

Accepted Answer

g(x)=x2-5

Answer

g(x)=x2+5

Answer

g(x)=(x-5)²

Answer

g(x)=(x+5)²

Question 19

Blue is the parent function $$f\left(x\right)=x^2$$ .

Red is another function $$g\left(x\right)$$ .

What could be the equation for the RED function

Accepted Answer

g(x)=2x2

Answer

g(x)=0.5x²

Answer

g(x)=x2+2

Answer

g(x)=(x+2)²

Question 20

Which is the graph of $$f\left(x\right)=\left(x-4\right)^2$$

Accepted Answer

Question 21

What is the formula to find the axis of symmetry of a quadratic?

Accepted Answer

$$x=-\frac{b}{2a}$$

Answer

$$x=\frac{b}{2a}$$

Answer

$$x=\frac{a}{2b}$$

Answer

$$x=-\frac{a}{2b}$$

Question 22

What term describes the red line shown in the graph?

Accepted Answer

axis of symmetry

Answer

x-axis

Answer

maximum

Answer

y-intercept

Question 23

When would you use this form of a quadratic function:

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

Accepted Answer

When you know the vertex and at least one other point

Answer

When you know the x-intercepts

Answer

When you know 3 or 4 points anywhere on the graph

Answer

When you know the y-intercept

Question 24

Which is NOT a way to write a quadratic function?

Accepted Answer

$$f\left(x\right)=-\frac{b}{2a}$$

Answer

$$f\left(x\right)=ax^2+bx+c$$

Answer

$$f\left(x\right)=a\left(x-p\right)\left(x-q\right)$$

Answer

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

Question 25

Which is the graph of $$f\left(x\right)=x^2-4$$

Accepted Answer

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