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

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 $$h = -5t^2$ + 20t. $$When will the ball hit the ground again?

Accepted Answer

$$t = 4$$

Question 3

Solve the equation $$x^2 - 7x + 12 = 0$ by factoring.

Accepted Answer

$$x = 3,\ x = 4$$

Question 4

Which of the following is the correct solution set for $$x^2 = 49$?

Accepted Answer

$$x = 7,\ x = -7$$

Question 5

Given the equation $$2x^2 + 4x - 6 = 0$, what is the value of x$ using the quadratic formula?

Accepted Answer

$$x = 1,\ x = -3$$

Question 6

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

Accepted Answer

$$t = 2,\ t = 4$$

Question 7

Solve $$x^2 + 2x = 63$ by completing the square.

Accepted Answer

$$x = 7,\ x = -9$$

Question 8

Which of the following is the correct solution to $$y^2 + 14y = -30$ using the quadratic formula?

Accepted Answer

$$y = -7 \pm \sqrt{19}$$

Question 9

A medical dosage is modeled by $$0.2x^2 - 1.2x = -2$. What is the solution for x$?

Accepted Answer

$$x = 3 \pm \sqrt{11}$$

Question 10

Solve $$x^2 + 4x + 13 = 0$ by completing the square.

Accepted Answer

$$x = -2 \pm 3i$$

Question 11

Which of the following is the correct solution set for $$x^2 - 4x + 11 = 0$ using the quadratic formula?

Accepted Answer

$$x = 2 \pm 3i$$

Question 12

Solve $$\frac{1}{2}x^2$ + 2x = 8 by $$multiplying both sides by 2 and using the quadratic formula.

Accepted Answer

$$x = -4 \pm 4\sqrt{3}$$

Question 13

A projectile's height is modeled by $$h = -16t^2$ + 32t + 48. $$When does it reach the ground?

Accepted Answer

$$t = -1,\ t = 3$$

Question 14

Solve $$x^2 - 2x = 63$ by completing the square.

Accepted Answer

$$x = 1 \pm 8$$

Question 15

Which of the following is the correct solution for $$x^2 + 6x + 10 = 0$?

Accepted Answer

$$x = -3 \pm i$$

Question 16

Solve $$x^2 - 8x + 20 = 0$ using the quadratic formula.

Accepted Answer

$$x = 4 \pm 2i$$

Solving Quadratic Equations: Methods and Applications

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