Question 1

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

Accepted Answer

$$x = -\frac{3}{2}$$

Question 2

For the quadratic function $$f(x) = -x^2$ + 4x - 5$$, what is the vertex?

Accepted Answer

$$(2, -1)$$

Question 3

Which of the following describes the direction in which the parabola $$f(x) = -2(x-1)^2$ + 3$$ opens?

Accepted Answer

Downward

Question 4

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

Accepted Answer

$$(-\infty, 4]$$

Question 5

If a quadratic function is written in vertex form $$f(x) = a(x-h)^2$ + k$$, what does the value of $$a$$ determine?

Accepted Answer

The direction and width of the parabola

Question 6

Given $$f(x) = 3(x+2)^2$ - 5$$, what is the minimum or maximum value of the function?

Accepted Answer

Minimum at $$y = -5$$

Question 7

Which transformation occurs when the function $$f(x) = (x-4)^2$ + 2 is $$compared to $$f(x) = x^2$?

Accepted Answer

Shift right 4 units and up 2 units

Question 8

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 9

Convert the quadratic function $$f(x) = x^2$ - 6x + 5 to $$vertex form.

Accepted Answer

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

Question 10

For the function $$f(x) = -2x^2$ + 8x - 6$$, over which interval is the function increasing?

Accepted Answer

$$(-\infty, 2]$$

Question 11

What is the domain of any quadratic function?

Accepted Answer

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

Question 12

Which of the following is the correct formula for the axis of symmetry of $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

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

Question 13

A parabola models the path of a thrown object. If the vertex is at $$(3, 7)$$, what does this point represent in the context of the object's motion?

Accepted Answer

The highest point reached by the object

Question 14

Given $$f(x) = 2x^2$ - 8x + 6$$, what is the y-intercept?

Accepted Answer

$$6$$

Question 15

Which of the following quadratic functions has a vertex at $$(1, -2)$$?

Accepted Answer

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

Question 16

If $$f(x) = -3(x+2)^2$ + 4$$, what is the domain and range of $$f(x)$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, 4]$$

Question 17

Which method can be used to convert a quadratic function from standard form to vertex form?

Accepted Answer

Completing the square

Question 18

For $$f(x) = x^2$ - 4x + 7$$, what is the vertex?

Accepted Answer

$$(2, 3)$$

Question 19

If $$f(x) = -x^2$ + 6x - 8$$, over which interval is the function decreasing?

Accepted Answer

$$[3, \infty)$$

Question 20

A company models its profit with $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of items sold. What is the maximum profit?

Accepted Answer

$$52$$

Quadratic Functions: Properties, Vertex Form, and Graphing Techniques

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