Question 1

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

Accepted Answer

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

Question 2

Given the quadratic function $$f(x) = 2x^2$ + 3x - 7$$, what is the degree of the polynomial?

Accepted Answer

$$2$$

Question 3

For the quadratic function $$f(x) = a(x - h)^2$ + k$$, what is the vertex of the parabola?

Accepted Answer

$$(h, k)$$

Question 4

If the graph of $$f(x) = -x^2$ + 4x - 5$$ opens downward, which value of $$a$$ causes this?

Accepted Answer

$$a \u003c 0$$

Question 5

What is the axis of symmetry for the quadratic function $$f(x) = 3(x + 2)^2$ - 5$$?

Accepted Answer

$$x = -2$$

Question 6

A ball is thrown and its height is modeled by $$h(t) = -16t^2$ + 32t + 5. $$What is the maximum height reached by the ball?

Accepted Answer

$$h(1) = -16(1)^2$ + 32(1) + 5 = 21$$

Question 7

Which transformation occurs when the function $$f(x) = (x - 3)^2$ + 2 is $$compared to $$f(x) = x^2$?

Accepted Answer

Shift left 3 units and up 2 units

Question 8

Given $$f(x) = -2(x + 1)^2$ + 6$$, what is the vertex and does the parabola have a maximum or minimum?

Accepted Answer

Vertex $$(-1, 6)$$, maximum

Question 9

What is the domain and range of $$f(x) = x^2$ + 1$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[1, \infty)$$

Question 10

A company models its profit by $$P(x) = -x^2$ + 6x + 7$$, where $$x is $$the number of items sold. How many items should be sold to maximize profit?

Accepted Answer

$$x = 3$$

Question 11

Convert $$f(x) = x^2$ + 6x + 7 to $$vertex form.

Accepted Answer

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

Question 12

For $$f(x) = 2x^2$ - 4x + 1$$, what is the axis of symmetry?

Accepted Answer

$$x = 1$$

Question 13

Which method is best to use for solving $$f(x) = x^2$ + 3x + 2$$ for its roots?

Accepted Answer

Factoring

Question 14

If $$f(x) = a(x - h)^2$ + k$$ and $$|a| \u003c 1$$, what effect does this have on the graph?

Accepted Answer

Vertical compression

Question 15

Given $$f(x) = (x - 2)^2$ + 4$$, what is the $$y-$$intercept?

Accepted Answer

$$f(0) = 8$$

Question 16

A parabola has vertex $$(3, -2)$$ and opens upward. Which equation could represent its function?

Accepted Answer

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

Question 17

Which of the following describes the interval where $$f(x) = x^2$ is increasing?

Accepted Answer

$$x \u003e 0$$

Question 18

For $$f(x) = -x^2$ + 2x + 3$$, what is the range of the function?

Accepted Answer

$$(-\infty, 4]$$

Question 19

If a parabola opens downward and has a vertex at $$(0, 5)$$, what is the maximum value of the function?

Accepted Answer

$$5$$

Question 20

Which of the following is NOT a property of all quadratic functions?

Accepted Answer

They always open upward.

Quadratic Functions: Properties, Vertex Form, and Transformations

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