Lesson: Solving Quadratic Equations & Inequalities

UNIT 6 (1) Solving Quadratic Functions

Unit Name: Polynomials

Lesson: Solving Quadratic Equations & Inequalities

Quadratic equations have the form

We are going to solve for the values of x algebraically. Those answers are the x-value of the x-intercept. It is where the graph crosses the x-axis. That is true for the solution of any polynomial equation.

UNIT 6 (1) Solving Quadratic Functions

Methods for solving 1. Factoring 2. Square Root Property 3. Completing the Square 4. Quadratic Formula 5. Graphing

Solving by Factoring 1.

2.

UNIT 6 (1) Solving Quadratic Functions

Solving by Square Root Property 1.

2.

3.

Solving by Completing the Square 1.

2.

UNIT 6 (1) Solving Quadratic Functions

Solving by Quadratic Formula 1.

2.

Solve by Square Root Property 5)

Solve by Factoring 1) 2)

6)

Solve by Completing The Square

3) 4)

Solve by Quadratic Formula

7) 8)

UNIT 6 (1) Solving Quadratic Functions

Graphing Method #1 Type the equation into y= and graph. Note the number of solutions you are looking for. Check the table for where the y values are zero. These are the values of the x-intercepts (roots or zeroes)

1.

2.

so

UNIT 6 (1) Solving Quadratic Functions

Graphing Method #2 Type the equation into y= and graph. Use the CALC function to find the zeroes.

3)

4)

Solving Quadratic Inequalities 1)

UNIT 6 (1) Solving Quadratic Functions

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4)