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 $(x-7)^2 = 49$?

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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