Question 1

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

Accepted Answer

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

Question 2

Given the quadratic equation $$x^2 + 10x + 2 = 0$, which method would be most appropriate to solve it?

Accepted Answer

Completing the square

Question 3

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what can you conclude about its solutions?

Accepted Answer

There are two non-real complex solutions

Question 4

Solve the equation $$x^2 - 29 = 0$ using the square root property.

Accepted Answer

$$x = \pm \sqrt{29}$$

Question 5

A chemical reaction produces a quadratic equation for the concentration of a product: $$2x^2 + 10x - 20 = 0$. What are the concentrations (values of x$) using the quadratic formula?

Accepted Answer

$$x = 1$$ and $$x = -10$$

Question 6

Which of the following best describes the Zero-Factor Property?

Accepted Answer

If $$ab = 0$$, then $$a = 0 or$$ $$b = 0 or $$both

Question 7

Given $$x^2 - 8x = 24$, what is the first step in solving by completing the square?

Accepted Answer

Add $$(\frac{8}{2})^2$ = 16 to $$both sides

Question 8

A right triangle has a hypotenuse of 13 cm. One leg is 7 cm less than the other. What are the lengths of the legs?

Accepted Answer

12 cm and 5 cm

Question 9

For the function $$f(x) = 4x^2$ - 3x + 5$$, what are the zeros?

Accepted Answer

$$x = \frac{3 \pm \sqrt{-76}}{8}$$

Question 10

Which statement about the discriminant is correct?

Accepted Answer

If $$b^2 - 4ac = 0$, there is one real double root

Question 11

Solve $$x^2 + 6x = 3$ by completing the square.

Accepted Answer

$$x = -3 \pm \sqrt{6}$$

Question 12

Which equation is quadratic in form?

Accepted Answer

$$x^4$$ - $$2x^2 + 18x - 29 = 0$

Question 13

A medical dosage calculation leads to the equation $$x^2 - 144 = 0$. What is the correct solution for x$?

Accepted Answer

$$x = \pm 12$$

Question 14

If a quadratic equation $$ax^2 + bx + c = 0$ has a discriminant of -7$, what type and how many solutions does it have?

Accepted Answer

Two non-real complex solutions

Question 15

Solve $$x^2 - 4x + 6 = 5$ by completing the square.

Accepted Answer

$$x = 2 \pm i$$

Question 16

Which step is NOT part of solving a quadratic equation by completing the square?

Accepted Answer

Multiply both sides by $$a$$

Question 17

A projectile's height is modeled by $$h(t) = -16t^2$ + 32t + 80. $$When does it hit the ground?

Accepted Answer

$$t = 5$$ and $$t = -1$$

Question 18

Which of the following is the correct quadratic formula?

Accepted Answer

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

Question 19

If $$x^2 + 2x + 1 = 0$, what are the solutions?

Accepted Answer

$$x = -1$$

Quadratic Equations, Functions, Zeros, and Models: Study Notes

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