Question 1

Which of the following equations is NOT a quadratic equation?

Accepted Answer

$$x + 1 = 0$$

Question 2

A ball is thrown upward from the ground with an initial velocity such that its height $$h (in $$meters) after $$t$$ seconds is given by $$h = -4.9t^2$ + 20t. $$When will the ball hit the ground again?

Accepted Answer

$$t = 0 or$$ $$t = 4.08$$

Question 3

Solve the equation $$x^2 - 5x = -6$ by factoring.

Accepted Answer

$$x = -1 or$$ $$x = 6$$

Question 4

Which of the following is the correct application of the square root property to solve $$(x-3)^2 = 16$?

Accepted Answer

$$x = 3 \pm 4$$

Question 5

What is the discriminant of the equation $$2x^2 - 8x + 3 = 0$ and what does it tell you about the solutions?

Accepted Answer

The discriminant is $$40$$, so there are two distinct real solutions.

Question 6

Solve $$2x^2 - 8 = 0$ using the square root property.

Accepted Answer

$$x = 2 or$$ $$x = -2$$

Question 7

A chemical reaction's rate is modeled by $$r = t^2$ - 6t + 8 = 0$$, where $$t is $$time in seconds. When is the rate zero?

Accepted Answer

$$t = 2 or$$ $$t = 4$$

Question 8

Which of the following best describes the number and type of solutions for the equation $$x^2 + 4x + 8 = 0$?

Accepted Answer

Two complex (non-real) solutions

Question 9

Solve $$x^2 + 10 = 7x$ by completing the square.

Accepted Answer

$$x = \frac{7 \pm \sqrt{9}}{2}$$

Question 10

Given the quadratic equation $$x^2 - 6x = -10$, what are the solutions using the quadratic formula?

Accepted Answer

$$x = 3 \pm \sqrt{19}$$

Question 11

A projectile is launched and its height $$h in $$meters after $$t$$ seconds is given by $$h = -5t^2$ + 20t + 15. $$When will the projectile reach a height of $$15$$ meters again?

Accepted Answer

$$t = 0 or$$ $$t = 4$$

Question 12

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

Accepted Answer

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

Question 13

If the discriminant of a quadratic equation is zero, what can you conclude about its solutions?

Accepted Answer

There is one real solution (a repeated root).

Question 14

Solve $$2x^2 + 8x - 10 = 0$ by completing the square.

Accepted Answer

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

Question 15

A quadratic equation has a discriminant of $$-12. $$What does this tell you about its solutions?

Accepted Answer

There are two complex (non-real) solutions.

Question 16

Which of the following is a correct first step to solve $$x^2 + 10 = 7x$ by completing the square?

Accepted Answer

Rewrite as $$x^2 - 7x = -10$ and then add $$(\frac{7}{2}$$)^2 to $$both sides

Question 17

Solve $$x^2 = 25$ using the square root property.

Accepted Answer

$$x = 5 or$$ $$x = -5$$

Question 18

Which of the following equations can be solved by factoring as the most efficient method?

Accepted Answer

$$2x^2 - 8x = 0$

Question 19

A quadratic equation models the profit $$P (in $$dollars) for a company as $$P = -2x^2$ + 12x + 20$$, where $$x is $$the number of units sold. For what values of $$x$$ will the profit be zero?

Accepted Answer

$$x = -2 or$$ $$x = 10$$

Question 20

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

Accepted Answer

Dividing both sides by $$x$$

Quadratic Equations: Definitions, Methods, and Properties

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