Q: Which of the following is the correct definition of a quadratic equation in one variable?

$$ax^2 + bx + c = 0$, where a$$ \neq 0$$

Question 1

Which of the following is the correct definition of a quadratic equation in one variable?

Accepted Answer

$$ax^2 + bx + c = 0$, where a$$ 
eq 0$$

Question 2

Given the equation $$x^2 - 16 = 0$, which property is most appropriate to solve for x$?

Accepted Answer

Square Root Property

Question 3

If $$(x-3)(x-4) = 0$$, what are the solutions for $$x$$?

Accepted Answer

$$x = 3 or$$ $$x = 4$$

Question 4

Which step is necessary before applying the Zero Product Property to solve $$2x^2 - 8x = 0$?

Accepted Answer

Factor the equation

Question 5

Solve the equation $$x^2 = 36$ using the square root property.

Accepted Answer

$$x = 6 or$$ $$x = -6$$

Question 6

What is the solution to $$2x^2 + 72 = 0$?

Accepted Answer

$$x = 6i or$$ $$x = -6i$$

Question 7

Which of the following is the correct application of the addition property of equality to solve $$x^2 - 17x = -12$?

Accepted Answer

$$x^2 - 17x + 12 = 0$

Question 8

Given the quadratic equation $$ax^2 + bx + c = 0$, what is the discriminant?

Accepted Answer

$$D = b^2$ - 4ac$$

Question 9

If the discriminant $$D of a $$quadratic equation is negative, what can be said about its solutions?

Accepted Answer

There are two complex solutions

Question 10

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

Accepted Answer

$$t \approx 4.2$$ seconds

Question 11

Which method is best for solving $$x^2 - 6x + 9 = 0$?

Accepted Answer

Factoring

Question 12

What is the solution to $$(x-7)^2 = 49$?

Accepted Answer

Question 13

Which of the following is the correct first step to solve $$x^2 + 8x + 15 = 0$ by factoring?

Accepted Answer

Find two numbers that multiply to 15 and add to 8

Question 14

A chemical reaction's rate is modeled by $$r = t^2$ - 4t + 3. At $$what time $$t is $$the rate zero?

Accepted Answer

$$t = 1 or$$ $$t = 3$$

Question 15

Which equation is equivalent to $$x^2 = c$?

Accepted Answer

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

Question 16

If $$x^2 + 2x - 8 = 0$, what are the solutions for x$?

Accepted Answer

$$x = -4 or$$ $$x = 2$$

Question 17

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 18

A medical dosage is modeled by $$d = x^2$ - 5x + 6. $$For which values of $$x is $$the dosage zero?

Accepted Answer

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

Question 19

Which of the following is a necessary condition for the Zero Product Property to be used?

Accepted Answer

The equation must be set equal to zero

Question 20

If $$x^2 - 9 = 0$, which real-world scenario could this model?

Accepted Answer

The distance from a point to a reference is 3 units

Solving Quadratic Equations: Zero Product and Square Root Properties

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