Question 1

Solve the equation $$(7x + 2)^2 = 9$$ using the square root property. What are the solutions?

Accepted Answer

$$x = 1,\ x = -\frac{4}{7}$$

Question 2

Determine the number and type of solutions for the equation $$2x^2 = 8x - 8.$$

Accepted Answer

Two real solutions

Question 3

Solve the equation $$x^2 = -6x + 2$$ using the quadratic formula. Give your answer in simplified radical form.

Accepted Answer

$$x = 3 \pm \sqrt{11}$$

Question 4

Rationalize the denominator: $$\frac{13}{\sqrt{19}}.$$

Accepted Answer

$$\frac{13\sqrt{19}}{19}$$

Question 5

Given the function $$f(x) = (x + 4)^2 + 2$$, what is the domain?

Accepted Answer

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

Question 6

Given the function $$f(x) = (x + 4)^2 + 2$$, what is the range?

Accepted Answer

$$[2, \infty)$$

Question 7

For the function $$f(x) = x^2 - 8x + 15$$, what are the x-intercepts?

Accepted Answer

$$(5, 0)$$ and $$(3, 0)$$

Question 8

For the function $$f(x) = x^2 - 8x + 15$$, what is the vertex?

Accepted Answer

$$(4, -1)$$

Question 9

Simplify $$\sqrt{54}. $$Leave your answer in simplified radical form.

Accepted Answer

$$3\sqrt{6}$$

Question 10

You have 180 feet of fencing to enclose a rectangular plot that borders a river (so you do not fence the side along the river). What are the dimensions that maximize the area?

Accepted Answer

Length = 90 ft, Width = 45 ft

Question 11

What is the maximum area that can be enclosed with 180 feet of fencing along a river (with no fence on the river side)?

Accepted Answer

$$4050\ 	ext{ft}^2$$

Question 12

Find the value of $$c$$ that makes $$x^2 + 8x + c$ a perfect-square trinomial, and factor the trinomial.

Accepted Answer

$$c = 16;\ (x + 4)^2$$

Question 13

Which of the following best describes the discriminant $$b^2 - 4ac$ for the equation 2x^2$ = 8x - 8$$?

Accepted Answer

It is positive, so there are two real solutions.

Question 14

A company wants to build a rectangular garden along a straight river, using 180 feet of fencing for three sides. Which equation models the area $$A in $$terms of the width $$w$$?

Accepted Answer

$$A = w(180 - 2w)$$

Question 15

If the quadratic equation $$x^2 + bx + c = 0$ has no real solutions, what can you say about the discriminant?

Accepted Answer

$$b^2 - 4ac \u003c 0$$

Intermediate Algebra: Quadratics, Graphing, and Optimization Review

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