Question 1

Which of the following best describes the vertex of the quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

The vertex is at $$x = -\frac{b}{2a}.$$

Question 2

Given the quadratic function $$f(x) = -2x^2$ + 4x - 1$$, which way does its graph open?

Accepted Answer

Downward, because $$a \u003c 0.$$

Question 3

Which of the following statements about the line $$x = -\frac{b}{2a}$$ for a quadratic function is TRUE?

Accepted Answer

It is the axis of symmetry of the parabola.

Question 4

A secant line to a curve is best described as:

Accepted Answer

A line that passes through two points on the curve.

Question 5

Which of the following is the correct formula for the average rate of change of $$f(x)$$ from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$\frac{f(x_2$) - f(x_1$)}{x_2$ - x_1$}$$

Question 6

For the function $$f(x) = x^2$ - 4x + 3$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = 2$$

Question 7

Which of the following best describes a tangent line to a curve at a point?

Accepted Answer

A line that touches the curve at exactly one point and has the same slope as the curve at that point.

Question 8

If $$f(x) = x^2$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = 0$$

Question 9

Which of the following is NOT true about the graph of a quadratic function?

Accepted Answer

It is always a straight line.

Question 10

For $$f(x) = 2x^2$ - 8x + 5$$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 11

Which of the following real-world scenarios is best modeled by a quadratic function?

Accepted Answer

The height of a ball thrown upward as a function of time.

Question 12

If the graph of $$f(x) = ax^2$ + bx + c$$ opens downward, which of the following must be true?

Accepted Answer

$$a \u003c 0$$

Calculus Study Notes: Functions, Limits, and Differentiation

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