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

Given the equation $$x^2 + 5x = -2$, what are the values of a$, b$, and c$ when rewriting it in standard form ax^2$ + bx + c = 0$$?

Accepted Answer

$$a = 1, b = 5, c = 2$$

Question 3

Solve $$x^2 + 5x + 2 = 0$ using the quadratic formula. What is the solution?

Accepted Answer

$$x = \frac{-5 \pm \sqrt{17}}{2}$$

Question 4

For the equation $$4x^2 - 6x - 1 = 0$, what is the value under the square root (the discriminant) in the quadratic formula?

Accepted Answer

$$b^2 - 4ac = 36 + 16 = 52$

Question 5

What are the solutions to $$4x^2 - 6x - 1 = 0$ using the quadratic formula?

Accepted Answer

$$x = \frac{3 \pm \sqrt{13}}{4}$$

Question 6

If the discriminant $$b^2 - 4ac$ is negative, what does this indicate about the solutions to the quadratic equation?

Accepted Answer

There are two complex (non-real) solutions.

Question 7

Solve $$x^2 - x + 5 = 0$ using the quadratic formula. What is the solution?

Accepted Answer

$$x = \frac{1 \pm i\sqrt{19}}{2}$$

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 will the ball hit the ground again?

Accepted Answer

$$t = 4$$ seconds

Question 9

Which of the following real-world scenarios can be modeled by a quadratic equation?

Accepted Answer

The path of a projectile in the air.

Question 10

If $$x^2 + bx + c = 0$ has two equal real roots, what must be true about the discriminant?

Accepted Answer

$$b^2 - 4c = 0$

Question 11

A chemical reaction's rate is modeled by $$r = -2t^2$ + 8t + 3. At $$what time $$t$$ does the reaction rate reach its maximum?

Accepted Answer

$$t = 2$$

Question 12

Which of the following is NOT a possible outcome when solving a quadratic equation using the quadratic formula?

Accepted Answer

Three real solutions

Question 13

A rectangular garden has an area of $$24 m$^2$$ and its length is $$2$$ meters longer than its width. Which quadratic equation models this scenario?

Accepted Answer

$$x^2 + 2x - 24 = 0$

Question 14

If the quadratic equation $$ax^2 + bx + c = 0$ has a = 2$, b = -4$, and c = 2$, what are the solutions?

Accepted Answer

$$x = 1$$

Question 15

Which step is necessary before applying the quadratic formula to $$x^2 + 3x = 7$?

Accepted Answer

Rewrite as $$x^2 + 3x - 7 = 0$

Solving Quadratic Equations Using the Quadratic Formula

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