Question 1

Which of the following is the standard form of a quadratic equation?

Accepted Answer

$$ax^2 + bx + c = 0$

Question 2

A projectile is launched from the ground and its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t. $$After how many seconds does the projectile reach its maximum height?

Accepted Answer

$$t = 2.04$$

Question 3

Which equation represents a circle with center at $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 4

Which of the following is NOT a function?

Accepted Answer

$$x = y^2$

Question 5

Given the function $$f(x) = 2x - 5$$, what is $$f^{-1}(x$$)$$, the inverse function?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 5}{2}$$

Question 6

A line passes through the points $$(1, 2)$$ and $$(3, 8). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 3x - 1$$

Question 7

Which of the following best describes the graph of $$y = x^2$ - 4x + 3$$?

Accepted Answer

A parabola opening upwards with vertex at $$(2, -1)$$

Question 8

If the equation of a circle is $$x^2$$ + $$y^2 - 6x + 8y + 9 = 0$, what are the coordinates of its center?

Accepted Answer

$$(3, -4)$$

Question 9

Which of the following is the slope-intercept form of the equation of a line passing through $$(0, 5)$$ with slope $$-2$$?

Accepted Answer

$$y = -2x + 5$$

Question 10

A company’s profit $$P (in $$dollars) from selling $$x$$ units is given by $$P(x) = -2x^2$ + 40x - 100. $$How many units should the company sell to maximize profit?

Accepted Answer

$$x = 10$$

Question 11

Which of the following points lies on the circle with equation $$(x - 1)^2$ + (y + 2)^2$ = 16$$?

Accepted Answer

$$(5, -2)$$

Question 12

If $$f(x) = x^2$ and g(x) = x + 3$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$25$$

Question 13

Which of the following is the equation of a line parallel to $$y = 4x - 7$$ and passing through $$(2, 3)$$?

Accepted Answer

$$y = 4x - 5$$

Question 14

A real-world application: The path of a thrown ball can be modeled by $$h(t) = -16t^2$ + 32t + 5$$, where $$h is $$the height in feet and $$t is $$the time in seconds. What is the maximum height the ball reaches?

Accepted Answer

$$37$$ feet

College Algebra: Key Concepts and Study Guide

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