SOLVING QUADRATICS

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

For polynomials, how is factoring related to multiplying? 2x 2 – 3x – 5

Falling Objects! Use h = -16t 2 + h 0 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?

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. Example: 1

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

Find the discriminant and determine the number & types of roots. Example: 3

Example 4 Use the quadratic formula to find the zeros.

Example 5: Use the quadratic formula to find the zeros.

Example 6: Use the quadratic formula to find the zeros.

Practice Problems:

Completing the Square ax 2 + bx + c = 0 Is another way to solve a quadratic equation. a needs to be 1. b is easier when even. c needs to be moved to the other side of the = sign

Example 7:

Example 8:

Practice Problems