Question 1

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 2

What is the discriminant of the quadratic equation $$2x^2 - 4x + 1 = 0$ and what does it tell you about the solutions?

Accepted Answer

$$D = (-4)^2$ - 4 \cdot 2 \cdot 1 = 8$$, two real solutions

Question 3

Which factoring method is most appropriate for $$x^2 - 9$?

Accepted Answer

Difference of squares

Question 4

Solve $$x^2 + 12x = 0$ by factoring.

Accepted Answer

$$x = 0,\ x = -12$$

Question 5

Which of the following equations can be solved using the square root property?

Accepted Answer

$$x^2 = 25$

Question 6

What are the solutions to $$x^2 = -16$?

Accepted Answer

$$x = 4i,\ x = -4i$$

Question 7

Complete the square to solve $$x^2 + 6x + 5 = 0$.

Accepted Answer

$$x = -1,\ x = -5$$

Question 8

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 9

Which of the following is the correct step to complete the square for $$x^2 + 8x = 0$?

Accepted Answer

Add $$16 to $$both sides to get $$x^2 + 8x + 16 = 16$

Question 10

Given the quadratic equation $$x^2 - 4x + 4 = 0$, what is the nature of its solutions?

Accepted Answer

One real repeated solution

Question 11

Which of the following is a correct application of the AC method for factoring $$6x^2 + 11x + 3$?

Accepted Answer

Find two numbers that multiply to $$18$$ and add to $$11$$

Question 12

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

Accepted Answer

The equation has two complex (imaginary) solutions.

Question 13

Solve $$2x^2 + 7x + 6 = 0$ by factoring.

Accepted Answer

$$x = -2,\ x = -1.5$$

Question 14

Which of the following is the correct first step in solving $$x^2 + 4x - 5 = 0$ by completing the square?

Accepted Answer

Add $$5 to $$both sides to get $$x^2 + 4x = 5$

Question 15

A projectile is launched from a height of $$10$$ meters with an initial velocity of $$15 m/s. $$Its height $$h$$ after $$t$$ seconds is $$h = -5t^2$ + 15t + 10. $$When does it hit the ground?

Accepted Answer

$$t = 3.0$$ seconds

Question 16

Which of the following quadratics cannot be factored using real numbers?

Accepted Answer

$$x^2 + 4$

Question 17

If $$x^2 + bx + 9 = 0$ has exactly one real solution, what is the value of b$?

Accepted Answer

$$b = 6 or$$ $$b = -6$$

Question 18

Which of the following is the correct way to check your solutions after factoring a quadratic equation?

Accepted Answer

Substitute the solutions back into the original equation to verify they satisfy it.

Question 19

What is the sum of the solutions to $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$5$$

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

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