Question 1

Which of the following equations is in standard form for a quadratic equation?

Accepted Answer

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

Question 2

A ball is thrown upward from the ground with an initial velocity. Its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t. $$After how many seconds does the ball hit the ground again?

Accepted Answer

$$t = 4.08$$

Question 3

Which of the following statements about the discriminant $$b^2 - 4ac$ of a quadratic equation ax^2$ + bx + c = 0 is $$correct?

Accepted Answer

If $$b^2 - 4ac$$ \u003c 0$$, there are two complex conjugate solutions.

Question 4

Solve the equation $$2x^2 - x = 3$ using the principle of zero products.

Accepted Answer

$$x = -1 or$$ $$x = \dfrac{3}{2}$$

Question 5

Which of the following is the correct application of the principle of square roots to solve $$x^2 = 9$?

Accepted Answer

$$x = \pm 3$$

Question 6

A quadratic equation $$ax^2 + bx + c = 0$ has only one real solution. Which of the following must be true?

Accepted Answer

$$b^2 - 4ac = 0$

Question 7

Which of the following equations is reducible to quadratic form and can be solved by substitution?

Accepted Answer

$$x^4$$ - $$5x^2 + 4 = 0$

Question 8

Given the quadratic function $$f(x) = 3x^2$ + 2x - 7$$, use the quadratic formula to find the exact solutions for $$f(x) = 0.$$

Accepted Answer

$$x = \dfrac{-2 \pm \sqrt{88}}{6}$$

Question 9

A company models its profit $$P (in $$thousands of dollars) by the function $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). For what value of $$x$$ does the company break even (i.e., $$P(x) = 0$$)?

Accepted Answer

$$x = 1 or$$ $$x = 8$$

Question 10

Which of the following best describes the zeros of the quadratic function $$f(x) = x^2$ + 4x + 5$$?

Accepted Answer

Two complex conjugate zeros

Question 11

Solve the equation $$x^2 - 10 = 0$ using the principle of square roots.

Accepted Answer

$$x = \pm \sqrt{10}$$

Question 12

A quadratic equation $$ax^2 + bx + c = 0$ has solutions x = 2$ and x = -3$. Which of the following could be the equation?

Accepted Answer

$$x^2 + x - 6 = 0$

Question 13

Which of the following is the correct first step in solving $$x^2 - 6x + 5 = 0$ by completing the square?

Accepted Answer

Move the constant to the other side: $$x^2 - 6x = -5$

Question 14

A real-world scenario: The number of magazine closures in a year is modeled by $$m(x) = 34x^2$ - 59x + 81$$, where $$x is $$the number of years after 2012. In what year were there 99 closures?

Accepted Answer

2014

Question 15

Which of the following is NOT a valid method for solving a quadratic equation?

Accepted Answer

Dividing both sides by $$x$$

Question 16

If $$x^4$$ - $$5x^2 + 4 = 0$, what are all the real solutions?

Accepted Answer

$$x = -2, -1, 1, 2$$

Question 17

Which of the following best describes the solutions to $$x^2 + 2x + 2 = 0$?

Accepted Answer

Two complex solutions

Question 18

What is the sum of the solutions to the quadratic equation $$3x^2 - 5x + 2 = 0$?

Accepted Answer

$$\dfrac{5}{3}$$

Question 19

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \dfrac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Quadratic Functions and Equations: Principles, Methods, and Applications

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