Question 1

Given the quadratic function $$y = x^2$ - 2x + 8$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 2

A ball is thrown upward with an initial speed of $$27 ft/sec $$from ground level. Its height $$h$$ after $$t$$ seconds is given by $$h = -16t^2$ + 27t. $$What is the maximum height reached by the ball?

Accepted Answer

$$22.78 ft$$

Question 3

Which of the following is the correct factorization of $$x^2 + 24x = 11$?

Accepted Answer

$$(x + 25)(x - 1) = 0$$

Question 4

Given the rational function $$f(x) = \frac{x}{x^2$ - 2x}$$, what is the domain of $$f(x)$$?

Accepted Answer

All real numbers except $$x = 0$$ and $$x = 2$$

Question 5

A quadratic function has its vertex at $$(1, -5)$$ and passes through the point $$(4, 4). $$What is its equation?

Accepted Answer

$$y = x^2$ - 2x - 2$$

Question 6

Solve the radical equation $$\sqrt{2x - 1} = x - 3.$$

Accepted Answer

$$x = 4$$

Question 7

A 50-foot supporting wire is to be attached to a 75-foot antenna. The wire must be anchored exactly 20 feet from the base of the antenna. How high from the base of the antenna is the wire attached?

Accepted Answer

$$51.96 ft$

Question 8

Given the quadratic equation $$x^2 + 24x = 11$, find the roots using the quadratic formula.

Accepted Answer

$$x = -12 \pm \sqrt{155}$$

Question 9

If a linear regression equation for the data $$\{(1, 6), (2, 8), (3, 10), (4, 12)\} is $$found, what is the slope of the regression line?

Accepted Answer

$$2$$

Question 10

Solve the rational equation $$\frac{2x}{x^2$ - 1} = \frac{3x}{x^2$ - 4}.$$

Accepted Answer

$$x = 0$$

Question 11

Given the function $$y = -2x^2$ + 4$$, which statement is true about its graph?

Accepted Answer

It opens downward and has a maximum at $$x = 0$$

Question 12

Find the $$x-$$intercepts of the quadratic function $$y = 3x^2$ + 22x - 18.$$

Accepted Answer

$$x = -9, x = 2/3$$

Question 13

Which of the following is the correct simplification of $$\frac{4x^2$ - x - 3}{2x^2$ + 3x - 2}$$?

Accepted Answer

$$\frac{(4x + 3)(x - 1)}{(2x - 1)(x + 2)}$$

Question 14

A rectangle has a length $$2$$ feet longer than its width. If the area is $$48$$ square feet, what is the length of the rectangle?

Accepted Answer

$$8 ft$$

Question 15

Solve the radical equation $$\sqrt{2x - 1} = x - 3$$ for $$x.$$

Accepted Answer

$$x = 4$$

Question 16

Given the quadratic function $$y = x^2$ - 2x + 8$$, what is the minimum value of the function?

Accepted Answer

$$7$$

Question 17

Which of the following is the correct solution to $$x^2 + 24x = 11$ using the quadratic formula?

Accepted Answer

$$x = -12 \pm \sqrt{155}$$

Question 18

If the sum of a quadratic function's roots is $$-a$$ and the product is $$b$$, what are the factors of the standard form $$x^2 + ax + b$?

Accepted Answer

$$(x + r_1$)(x + r_2$)$$ where $$r_1$$ + $$r_2 = -a$ and r_1$ r_2$ = b$$

College Algebra Review: Quadratic, Radical, and Rational Equations, Functions, and Graphs

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