Question 1

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

Accepted Answer

$$40.8$$ meters

Question 2

Which of the following is the correct vertex form for the quadratic equation $$y = 2x^2$ - 8x + 3$$?

Accepted Answer

$$y = 2(x - 2)^2$ - 5$$

Question 3

A quadratic equation $$x^2 - 6x + 9 = 0$ is solved by factoring. What are the real solutions?

Accepted Answer

$$x = 3$$

Question 4

Which of the following correctly applies the quadratic formula to solve $$2x^2 + 3x - 5 = 0$?

Accepted Answer

$$x = \frac{-3 \pm \sqrt{3^2$ - 4 \cdot 2 \cdot (-5)}}{2 \cdot 2}$$

Question 5

Which of the following is NOT a property of exponents?

Accepted Answer

$$a^m + a^n = a$$^{m+n}$$

Question 6

Consider the power function $$f(x) = -x^3$. Which statement is true about its graph?

Accepted Answer

It is concave down everywhere.

Question 7

Which of the following describes the domain of the function $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$x \geq 4$$

Question 8

If $$f(x) = x^2$ and g(x) = 2x + 1$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(2x + 1)^2$

Question 9

Kepler’s Third Law relates the period $$P$$ and the radius $$r of a $$planet’s orbit by $$P^2$$ = $$kr^3. If$$ $$k = 1$$ and $$r = 4$$, what is $$P$$?

Accepted Answer

$$P = \sqrt{64} = 8$$

Question 10

Solve the equation $$x^{1/2} = 9$ for x$.

Accepted Answer

$$x = 81$$

Question 11

Which transformation will shift the graph of $$f(x) = x^2$ up by 5 units and to the right by 3 units?

Accepted Answer

$$f(x) = (x - 3)^2$ + 5$$

Question 12

A piecewise function is defined as $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x + 1 & x \geq 0 \end{cases}. $$What is $$f(-2)$$?

Accepted Answer

$$4$$

Question 13

Which of the following is the range of the function $$f(x) = x^4$?

Accepted Answer

$$[0, \infty)$$

Question 14

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (g$$ \circ f)(x)$$?

Accepted Answer

$$x \in (-\infty, \infty)$$

Question 15

Which of the following is the correct solution to $$x^2 + 4x + 5 = 0$ using the quadratic formula?

Accepted Answer

$$x = -2 \pm i$$

Question 16

Which of the following is a correct example of combining power functions?

Accepted Answer

$$f(x) = x^2$ + x^3$

Question 17

A medical dosage is modeled by $$D(t) = 100e$$^{-0.1t}$$, where t$ is time in hours. What is the dosage after 5$ hours?

Accepted Answer

$$D(5) = 100e$$^{-0.5}$$

Question 18

Which of the following is the result of completing the square for $$x^2 + 6x + 8$?

Accepted Answer

$$(x + 3)^2$ - 1$$

Question 19

Which of the following statements about the function $$f(x) = x$$^{-2}$$ is true?

Accepted Answer

The function is decreasing for $$x \u003e 0.$$

Exam 2 Study Guide: Quadratic Equations, Power Functions, and Related Topics

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