Question 1

Given the graph of a parabola opening downward with vertex at $$(0, 5)$$ and passing through the points $$(-2, -11)$$ and $$(2, -11)$$, which of the following is the equation of the parabola?

Accepted Answer

$$y = -x^2$ + 5$$

Question 2

Which of the following best describes the vertex and axis of symmetry for the function $$f(x) = x^2$ + 6x + 8$$?

Accepted Answer

Vertex: $$(-3, -1)$$, Axis: $$x = -3$$

Question 3

Solve the equation $$x^2 - 6x + 9 = 0$ by factoring.

Accepted Answer

$$x = 3$$

Question 4

A baseball is thrown from a stadium and its height is modeled by $$h(x) = -16x^2$ + 32x + 128. $$How long will it take the ball to reach the ground?

Accepted Answer

$$x = 4 ($$rounded to the nearest hundredth)

Question 5

Simplify the radical expression $$\sqrt{420x^5$y^8$$}$.

Accepted Answer

$$2y^4x^2$\sqrt{105x}$

Question 6

Solve for $$x in $$the equation $$x^2 - 8x = 48$.

Accepted Answer

$$x = 12 or$$ $$x = -4$$

Question 7

A swimming pool has a length that is twice its width. There is a deck around the outside that has a uniform width of 2 ft. The total area of the pool and deck is $$96\ 	ext{ft}^2. $$What is the width of the pool?

Accepted Answer

$$4 ft$$

Question 8

Write the equation $$y = x^2$ + 20x + 90 in $$vertex form and state the minimum value.

Accepted Answer

Vertex form: $$y = (x + 10)^2$ - 10$$, Minimum: $$-10$$

Question 9

Solve the equation $$x^2 + 5x = -2$ using the quadratic formula.

Accepted Answer

$$x = \frac{-5 \pm \sqrt{33}}{2}$$

Question 10

What is the discriminant of $$5x^2 + 17 = 9x$ and what does it tell you about the roots?

Accepted Answer

Discriminant: $$41$$, Two real roots

Question 11

Perform the operation $$(5 - 2i) - 2(3 + i)$$ and write your answer in the form $$a + bi.$$

Accepted Answer

$$-1 - 4i$$

Question 12

Solve $$x^2 - 5 = 13$ using square roots.

Accepted Answer

$$x = \pm 6$$

Question 13

Given the function $$f(x) = x^2$ - 7x + 10$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 2$$ and $$x = 5$$

Question 14

If $$3x^2 + 12x + k = 0$ has two nonreal solutions, which of the following is true about k$?

Accepted Answer

$$k \u003e 36$$

Question 15

Donny throws a ball into the air. The height $$h of $$the ball, in meters, at time $$t$$ seconds is modeled by $$h(t) = -5t^2$ + 4t + 12. $$Will the ball reach a height of $$14$$ meters?

Accepted Answer

Yes, because the equation $$-5t^2 + 4t + 12 = 14$ has real solutions.

College Algebra Quadratic Equations and Graphs Study Guide

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