Question 1

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

Accepted Answer

$$2x^2 - 7x + 4 = 0$

Question 2

According to the Zero-Factor Property, if $$(x-3)(x+2) = 0$$, what are the possible values of $$x$$?

Accepted Answer

$$x = 3 or$$ $$x = -2$$

Question 3

Solve the equation $$x^2 = 5$ using the Square Root Property.

Accepted Answer

$$x = \pm \sqrt{5}$$

Question 4

Which value should be added to both sides to complete the square for $$x^2 + 8x$?

Accepted Answer

$$16$$

Question 5

What is the factored form of $$p^2 - 5p$?

Accepted Answer

$$p(p-5)$$

Question 6

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$After how many seconds does the ball hit the ground? (Round to two decimal places.)

Accepted Answer

$$t \approx 4.19$$

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

Solve $$3x^2 - 5x + 1 = 0$ using the quadratic formula. What is one of the solutions?

Accepted Answer

$$x = \frac{5 + \sqrt{13}}{6}$$

Question 9

Which of the following best describes the process of completing the square for $$x^2 + 12x$?

Accepted Answer

Add $$36 to $$both sides to form $$x^2 + 12x + 36$$ = $$(x+6)^2$$

Question 10

A company models its profit $$P (in $$thousands of dollars) by the equation $$P = -2x^2$ + 12x - 8$$, where $$x is $$the number of units sold (in thousands). For what value of $$x$$ does the company break even ($$P = 0$$)?

Accepted Answer

$$x = 1 or$$ $$x = 4$$

Question 11

If $$x^2 - 6x = 0$, what are the solutions?

Accepted Answer

$$x = 0 or$$ $$x = 6$$

Question 12

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

Accepted Answer

$$x^2 + x$$ + \frac{1}{4} = (x + \frac{1}{2}$$)^2$$

Question 13

A projectile is launched from the ground with an initial velocity such that its height after $$t$$ seconds is $$h(t) = -16t^2$ + 32t. $$When does it return to the ground?

Accepted Answer

$$t = 2$$

Question 14

Which of the following is the correct way to factor $$a^2 - 20a$?

Accepted Answer

$$a(a-20)$$

Question 15

If $$(x-2)^2 = 16$, what are the solutions for x$?

Accepted Answer

$$x = 2 \pm 4$$

Question 16

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

Accepted Answer

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

Question 17

Which of the following is the correct result when you complete the square for $$x^2 + 4x$?

Accepted Answer

$$x^2 + 4x + 4$$ = $$(x+2)^2$$

Question 18

If $$x^2 + 12x = 0$, what are the solutions?

Accepted Answer

$$x = 0 or$$ $$x = -12$$

Question 19

Which of the following is the correct result when you complete the square for $$x^2 + mx$?

Accepted Answer

$$x^2 + mx$$ + \left(\frac{m}{2}\$$right)^2$$ = \left(x + \frac{m}{2}\$$right)^2$$

Solving Quadratic Equations: Factoring, Completing the Square, and the Quadratic Formula

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