Question 1

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

Accepted Answer

$$x = -\frac{7}{2 	imes 3}$$

Question 2

For the function $$f(x) = 3x^2$ + 7x + 2$$, what is the discriminant and what does it tell you about the roots?

Accepted Answer

Discriminant is $$49 - 24 = 25$$, so there are two real roots.

Question 3

What is the vertex of the function $$f(x) = 3x^2$ + 7x + 2$$?

Accepted Answer

The vertex is at $$\left(-\frac{7}{6}, -\frac{13}{12}\right)$$

Question 4

A factory purchases a machine for $$\10$$,000$. It depreciates using the straight-line method over 10 years. What is the book value of the machine after 7 years?

Accepted Answer

$$\3$$,000$

Question 5

Given the depreciation scenario: A machine is purchased for $$\10$$,000$$ and depreciates to $$\$$0 in 10 $$years. What is the equation for the book value $$V as a $$function of time $$t in $$years?

Accepted Answer

$$V(t) = 10,000 - 1,000t$$

Question 6

What is the range of the function $$V(t) = 10,000 - 1,000t$$ for $$0 \leq t \leq 10$$?

Accepted Answer

$$[0, 10,000]$$

Question 7

An electronics company finds that when certain calculators are sold at a price of $$p$$ dollars each, the number of calculators sold is given by $$n = 750 - 30p. $$What price maximizes revenue?

Accepted Answer

$$p = 12.5$$

Question 8

For the revenue function $$R(p) = p(750 - 30p)$$, what is the maximum revenue?

Accepted Answer

$$4,687.50$$

Question 9

What is the domain of the function $$n = 750 - 30p if$$ $$n \geq 0$$?

Accepted Answer

$$0 \leq p \leq 25$$

Question 10

If the price per calculator is increased above the value that maximizes revenue, what happens to the revenue?

Accepted Answer

Revenue decreases because fewer calculators are sold.

Question 11

For the quadratic function $$f(x) = ax^2$ + bx + c$$, what is the formula for the vertex?

Accepted Answer

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

Question 12

If a quadratic function opens upwards and its discriminant is negative, what can you conclude about its graph?

Accepted Answer

The graph does not intersect the x-axis.

College Algebra Test 2 Review: Quadratic Functions, Vertex, Discriminant, and Applications

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