Question 1

Which of the following equations is a quadratic equation in $$x$$?

Accepted Answer

$$x^2 - 3x + 4 = 0$

Question 2

What is the zero-product principle used for when solving quadratic equations?

Accepted Answer

To set each factor equal to zero and solve for the variable

Question 3

Solve the quadratic equation by factoring: $$x^2 - 5x + 6 = 0$

Accepted Answer

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

Question 4

Which of the following is the correct application of the square root property to solve $$x^2 = 25$?

Accepted Answer

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

Question 5

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

Accepted Answer

$$64$$

Question 6

How many and what type of solutions does the equation $$x^2 + 4x + 5 = 0$ have?

Accepted Answer

Two imaginary solutions

Question 7

Solve the equation $$x^2 - 8x + 16 = 0$ using the quadratic formula.

Accepted Answer

$$x = 4$$

Question 8

A woman’s normal systolic blood pressure $$P at $$age $$A is $$modeled by $$P = 0.5A + 102. If $$her normal systolic blood pressure is $$115 mm Hg$$, what is her age to the nearest year?

Accepted Answer

$$A = 26$$

Question 9

Which method is most efficient for solving $$x^2 = 49$?

Accepted Answer

Square root property

Question 10

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

Accepted Answer

There is one real repeated solution

Question 11

A wheelchair ramp has a length of $$122$$ inches and a horizontal distance of $$120$$ inches. What is the vertical distance, $$x$$, to the nearest inch?

Accepted Answer

$$x = 17$$

Question 12

Construction law requires every vertical rise of $$1$$ inch to have a horizontal run of $$12$$ inches. Does the ramp with a $$17$$ inch rise and $$120$$ inch run satisfy this requirement?

Accepted Answer

No, because $$120 \div 17 \approx 7.1$$ which is less than $$12$$

Question 13

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 14

Which scenario best illustrates the use of the Pythagorean Theorem?

Accepted Answer

Calculating the diagonal distance across a rectangular field

Question 15

If $$a = 3$$, $$b = 4$$, and $$c is $$the hypotenuse of a right triangle, what is the value of $$c$$?

Accepted Answer

$$c = 5$$

Question 16

Which of the following best describes the discriminant in the quadratic formula?

Accepted Answer

The value under the square root sign, $$b^2 - 4ac$

Question 17

Solve for $$x$$: $$x^2 + 6x + 9 = 0$

Accepted Answer

$$x = -3$$

Question 18

Which of the following is NOT a valid method for solving quadratic equations?

Accepted Answer

Using the arithmetic mean

Question 19

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

Accepted Answer

$$t = 4.2$$

Quadratic Equations: Methods, Applications, and the Pythagorean Theorem

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