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: ______