Question 1

Which of the following is the general form of a quadratic function?

Accepted Answer

$$y = ax^2$ + bx + c$$

Question 2

Which of the following is the vertex form of a quadratic function?

Accepted Answer

$$y = a(x - h)^2$ + k$$

Question 3

On the provided graph, which letter corresponds to the vertex of the parabola?

Accepted Answer

c

Question 4

On the provided graph, which letter corresponds to the axis of symmetry?

Accepted Answer

d

Question 5

Given the quadratic $$y = 2x^2$ - 6x + 5$$, does the function have a minimum or maximum value?

Accepted Answer

A minimum

Question 6

Given the quadratic $$y = -3(x - 2)^2$ + 4$$, does the function have a minimum or maximum value?

Accepted Answer

A maximum

Question 7

Rewrite $$f(x) = x^2$ - 12x + 32 in $$vertex form and state the vertex.

Accepted Answer

$$f(x) = (x - 6)^2$ - 4$$, vertex: $$(6, -4)$$

Question 8

Find the solutions (roots/zeroes) of $$f(x) = x^2$ - 5x - 6.$$

Accepted Answer

$$x = -1, x = 6$$

Question 9

A baseball player throws a rock upward from a 112-foot cliff at 96 ft/s. The height is modeled by $$f(t) = -16t^2$ + 96t + 112. $$When does the rock reach its maximum height?

Accepted Answer

$$t = 3$$ seconds

Question 10

For the same scenario, what is the maximum height the rock reaches above the ocean?

Accepted Answer

$$256$$ feet

Question 11

For the same scenario, when does the rock hit the ocean (height = 0)?

Accepted Answer

$$t = 8$$ seconds

Question 12

You have 200 feet of fencing to build a rectangular enclosure. What should the length $$L$$ and width $$W be to $$maximize the area?

Accepted Answer

$$L = 50 ft$$, $$W = 50 ft$$

Question 13

Rewrite $$g(x) = 2x^2$ + 8x - 10 in $$vertex form and state the vertex.

Accepted Answer

$$g(x) = 2(x + 2)^2$ - 18$$, vertex: $$(-2, -18)$$

Question 14

Find the solutions (roots/zeroes) of $$g(x) = x^2$ + 4x + 5.$$

Accepted Answer

$$x = -2 + i, x = -2 - i$$

Question 15

Given $$h(x) = x^2$ - 2x$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 16

Given $$h(x) = x^2$ - 2x$$, what is the axis of symmetry?

Accepted Answer

$$x = 1$$

Question 17

Given $$h(x) = x^2$ - 2x$$, what is the domain of the function?

Accepted Answer

$$(-\infty, \infty)$$

Question 18

Given $$h(x) = x^2$ - 2x$$, what is the range of the function?

Accepted Answer

$$[-1, \infty)$$

Quadratic Functions: Forms, Properties, and Applications

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