Chapter 9: Solving Quadratic Equations

9.1: Solving Quadratic Equations by Graphing

Standard form of a Quadratic Equation: ______

One of these three things will happen when you graph a parabola:

______

______

______

Steps to Find the X-intercepts (also known as roots or zeros) of an equation:

1.) ______

2.)______

3.) ______

4.)______

Solving a Quadratic Equation: Two Real Solutions

Solve: x² - x - 6 =0

Solving a Quadratic Equation: One Real Solution

Solve: x²+9x=-20

Solving a Quadratic Equation: No Real Solutions

Solve: x² = -3x – 4

Real Life: function formula: h= -16t² +(velocity)t + initial height

A baseball player throws a baseball with an upward velocity of 20 feet per second. The release point is 6 feet above the ground. The function h= -16t²+20t+6 give the height h (in feet) of the baseball after t seconds.

a.) How long is the ball in the air if no one catches it?

b.) How long does the ball remain above 6 feet?

Name: ______

Period: ______

9.1 Desmos Activity:

·  Log onto www.desmos.com

·  Launch calculator

·  Graph the following

1.) y = x²+6x +1

Where does the graph cross the x axis:

______

What are the x-intercepts: ______

What are the zeros: ______

What are the roots: ______

2.) y = x² +2x - 3

Where does the graph cross the x axis:

______

What are the x-intercepts: ______

What are the zeros: ______

What are the roots: ______

3.) y= x² +6x +9

Where does the graph cross the x axis:

______

What are the x-intercepts: ______

What are the zeros: ______

What are the roots: ______

4.) y = x² + 4x + 5

Where does the graph cross the x axis:

______

What are the x-intercepts: ______

What are the zeros: ______

What are the roots: ______