Q: Which of the following is the correct definition of a quadratic equation in one variable?

$$ax^2 + bx + c = 0$, where a$$ \neq 0$$

Question 1

Which of the following is the correct definition of a quadratic equation in one variable?

Accepted Answer

$$ax^2 + bx + c = 0$, where a$$ 
eq 0$$

Question 2

Given the equation $$6x^2 - 17x = -12$, what is the first step to solve it by factoring?

Accepted Answer

Add 12 to both sides to set the equation to zero: $$6x^2 - 17x + 12 = 0$

Question 3

Which property allows you to conclude that if $$(x-3)(x+2) = 0$$, then $$x = 3 or$$ $$x = -2$$?

Accepted Answer

Zero Product Property

Question 4

Solve the equation $$x^2 - 16 = 0$ using the square root property.

Accepted Answer

$$x = 4 or$$ $$x = -4$$

Question 5

Which of the following is a perfect square trinomial, and how does it factor?

Accepted Answer

$$x^2 + 6x + 9 = (x$$ + $$3)^2$$

Question 6

What number must be added to $$x^2 - 12x$ to make it a perfect square trinomial?

Accepted Answer

36

Question 7

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 8

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

Accepted Answer

Discriminant is $$2^2 - 4$$ \cdot 3 \cdot 2 = -20$$, so there are two complex solutions.

Question 9

A ball is thrown upward from the ground with an initial velocity of 20 m/s. Its height $$h in $$meters after $$t$$ seconds is given by $$h = -5t^2$ + 20t. $$When does the ball hit the ground again?

Accepted Answer

$$t = 4$$ seconds

Question 10

Which of the following is the correct way to rationalize the denominator of $$\frac{1}{\sqrt{5}}$$?

Accepted Answer

$$\frac{\sqrt{5}}{5}$$

Question 11

If $$(x-1)^2 = 7$, what are the solutions for x$?

Accepted Answer

$$x = 1 + \sqrt{7} or$$ $$x = 1 - \sqrt{7}$$

Question 12

Which of the following is the correct factorization of $$x^2 + 5x + 6$?

Accepted Answer

$$(x + 2)(x + 3)$$

Question 13

Solve $$2x^2 + 72 = 0$ using the square root property.

Accepted Answer

$$x = 6i or$$ $$x = -6i$$

Question 14

Which of the following is the correct way to simplify $$\sqrt{-9}$$?

Accepted Answer

$$3i$$

Question 15

A quadratic equation $$ax^2 + bx + c = 0$ has a discriminant of zero. What does this indicate about its solutions?

Accepted Answer

There is exactly one real solution (a repeated root).

Question 16

Which of the following is the correct factorization of $$3x^2 + 2x - 2$?

Accepted Answer

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

Question 17

If $$4x^2 + 1 = 4x$, how many and what type of solutions does the equation have?

Accepted Answer

Two real solutions

Question 18

Which of the following is the correct simplification of $$\sqrt{50}$$?

Accepted Answer

$$\sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}$$

Question 19

A company models its profit $$P (in $$thousands of dollars) by the equation $$P = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). For what value of $$x$$ does the company break even (i.e., $$P = 0$$)?

Accepted Answer

$$x = -1 or$$ $$x = 5$$

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