# Algebra II : Quadratic Equations and Inequalities

## Example Questions

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### Example Question #1 : Simplifying And Expanding Quadratics

Solve the equation for .

Explanation:

Cross multiply.

Set the equation equal to zero.

Factor to find the roots of the polynomial.

and

Explanation:

### Example Question #2 : Simplifying And Expanding Quadratics

Solve the equation for :

Explanation:

1. Cross multiply:

2. Set the equation equal to :

3. Factor to find the roots:

,  so

, so

### Example Question #3 : Simplifying And Expanding Quadratics

If you were to solve  by completing the square, which of the following equations in the form   do you get as a result?

Explanation:

When given a quadratic in the form  and told to solve by completing the square, we start by subtracting from both sides. In this problem is equal to , so we start by subtracting  from both sides:

To complete the square we want to add a number to each side which yields a polynomial on the left side of the equals sign that can be simplified into a squared binomial . This number is equal to . In this problem is equal to , so:

We add  to both sides of the equation:

We then factor the left side of the equation into binomial squared form and combine like terms on the right:

### Example Question #4 : Simplifying And Expanding Quadratics

If you were to solve  by completing the square, which of the following equations in the form   do you get as a result?

Explanation:

When given a quadratic in the form  and told to solve by completing the square, we start by subtracting from both sides. In this problem is equal to , so we start by subtracting  from both sides:

To complete the square we want to add a number to each side which yields a polynomial on the left side of the equation that can be simplified into a squared binomial . This number is equal to . In this problem is equal to , so:

We add to both sides of the equation:

We then factor the left side of the equation into binomial squared form and combine like terms on the right:

### Example Question #3 : Binomials

Expand:

None of the other answers are correct.

Explanation:

Use the FOIL method, which stands for First, Inner, Outer, Last:

Multiply:

Explanation:

Multiply:

Explanation:

### Example Question #7 : Simplifying And Expanding Quadratics

Subtract:

Explanation:

When subtracting trinomials, first distribute the negative sign to the expression being subtracted, and then remove the parentheses:

Next, identify and group the like terms in order to combine them: .

### Example Question #3 : How To Multiply Trinomials

Evaluate the following: