Unit 3: Quadratic Equations

Question 1

Quadratic Equation

Answer 1

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.

Question 2

Rationalizing The Denominator

Answer 2

The process by which a fraction is rewritten so that the denominator contains only rational numbers.

Question 3

How many square roots do positive numbers have?

Answer 3

Positive numbers have two square roots, one negative and one positive, denoted by the plus-minus sign (±).

Question 4

Radical

Answer 4

The symbol, √ , a square root is written with.

Question 5

What is one method for rationalizing the denominator of a fraction?

Answer 5

A radical is not simplified if there is a radical in the denominator. One way correct this and further simplify the radical, you can multiply both the numerator and denominator by the denominator.

Question 6

How do you solve a quadratic equation using the square root property?

Answer 6

1. Isolate the power on one side of the equation.
2. Find the square root of each side.
3. Simplify the radical (if possible).
4. Isolate the variable.
   You are left with two possible solutions for the equation.

Question 7

How should you solve a quadratic equation in the form of a perfect square trinomial?

Answer 7

1. Factor the perfect square trinomial.
2. Use the square root property to find the square root of each side of the equation.
3. Simplify the radical (if possible).
4. Isolate the variable.
   You are left with two possible solutions for the equation.

Question 8

Completing The Square

Answer 8

The method of converting a quadratic equation which is not a perfect square into the sum or difference of a perfect square and a constant by adding or subtracting the suitable constant terms.

Question 9

Qaudratic Formula

Answer 9

a formula for finding the solutions of a quadratic equation in the form ax^2+bx+c=0 (a x squared plus b x plus c equals 0), where a is not zero.

Question 10

Qaudratic Formula

Answer 10

A formula for finding the solutions of a quadratic equation in the form ax^2+bx+c=0 (a x squared plus b x plus c equals 0), where a is not zero.

Question 11

Quadratic Formula

Answer 11

A formula for finding the solutions of a quadratic equation in the form ax^2+bx+c=0 (a x squared plus b x plus c equals 0), where a is not zero.

Question 12

Quadratic Formula

Answer 12

A formula for finding the solutions of a quadratic equation in the form ax^2+bx+c=0 (a x squared plus b x plus c equals 0), where a is not zero.

Question 13

Why might you discard a negative solution in a real-world problem?

Answer 13

You might discard a negative solution because certain factors, like distances, cannot be negative.

Question 14

What part of the quadratic formula is called the discriminant?

Answer 14

the expression b² −4 ac found under the radical symbol in a quadratic formula

Question 15

Quadratic Formula Method

Answer 15

A method in which quadratic equations in standard form are solved using the quadratic formula.

Question 16

Root(s) of an Equation

Answer 16

Solution(s) to an equation.

Question 17

Zero of a Function

Answer 17

The x-value for which f(x)=0

Question 18

Zero(s) of a Function

Answer 18

The x-value for which f(x)=0

Question 19

What part of the quadratic formula is called the discriminant?

Answer 19

the expression b² − 4ac found under the radical symbol in a quadratic formula.

Question 20

Zero(s) of a Function

Answer 20

The x-value for which f(x) = 0

Question 21

Discriminant Rules

Answer 21

1. Two rational solutions if the discriminant is positive and a perfect square.
2. Two irrational solutions if the discriminant is positive and not a perfect square.
3. One rational solution is the discriminant is equal to zero
4. No real solutions if the discriminant is negative.