Solving Quadratics.

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Presentation transcript:

Solving Quadratics

Factoring is fun!! USA Test Prep!!! Exceed!!! x2 +2x - 8 x2 +2x - 8 ( )( ) x x + 4 - 2 Factoring is fun!! USA Test Prep!!! Exceed!!!

Factoring is fun!! USA Test Prep!!! Exceed!!! x2 - 5x - 14 x2 - 5x - 14 ( )( ) x x - 7 + 2 Factoring is fun!! USA Test Prep!!! Exceed!!!

Factoring is fun!! USA Test Prep!!! Exceed!!! x2 – 5x - 24 x2 – 5x - 24 ( )( ) x x + 4 – 6 Factoring is fun!! USA Test Prep!!! Exceed!!!

Practice!! Use Calculator!! Factor each Polynomial !!!

Solving Quadratic Equations in Factored Form y = (x + 3)(x + 2) 0 = (x + 3)(x + 2) Ways to solve: y = x2 + 5x + 6 x-intercepts, roots, zero’s, solutions

Solve (Find the x-intercepts, roots, zeros, solutions) 1) x2 + 5x + 6 = 0 2) x2 – 2x – 8 = 0

For polynomials, how is factoring related to multiplying? Factor...Solve 2x2 – 3x – 5 2x2 – 3x – 5 For polynomials, how is factoring related to multiplying?

Practice……….

Solving Quadratic Equations by taking Square Roots……

PRACTICE……

Falling Objects! Use h = -16t2 + h0 Height of the object AFTER it has fallen TIME after the object has dropped Object’s INITIAL height

Example 11 The tallest building in the USA is in Chicago, Illinois. It is 1450 ft. tall. How long would it take a penny to drop from the top of the building to the ground?

Everything must be on the same side of the equals sign before solving Quadratic Formula Everything must be on the same side of the equals sign before solving

The Discriminant tells how many & what type of solutions the quadratic has.

Find the discriminant and determine the number & types of roots Find the discriminant and determine the number & types of roots. Example: 10 2 Imaginary Roots

Find the discriminant and determine the number & types of roots Find the discriminant and determine the number & types of roots. Example: 11 1 Real Root

Find the discriminant and determine the number & types of roots Find the discriminant and determine the number & types of roots. Example: 12 2 Real Roots

Example 13 Use the quadratic formula to find the zeros.

Example 14: Use the quadratic formula to find the zeros.

Example 15: Use the quadratic formula to find the zeros.

Practice Problems:

Solving Quadratic Inequalities Algebraically

Answers will look like: AND OR

1. Solve and graph.

2. Solve and graph.