Notes 2­3 Solving Quadratic Equations by Graphing and Factoring
Objectives:
­ Solve quadratic equations by graphing or factoring
­ Determine a quadratic function from its roots
Why learn this?
You can use quadratic functions to model the height of a football, baseball, or soccer ball. 1
A zero of a function is a value of the input x that makes the output f(x) equal zero.
The zeros of a function are the x­intercepts!
2
Ex. Find the zeros of by using a graph and table.
3
Try These:
Ex. Find the zeros of
by using a graph and a table. 4
The solutions to a quadratic equation of the form ax2 + bx + c = 0 are roots.
The roots of an equation are the values of the variable that make the equation true. 5
Ex. Find the zeros of each function by factoring.
a.
b.
6
Try These:
Ex. Find the zeros of each function by factoring.
a.
b.
7
Ex. Find the roots of each equation by factoring.
a.
b. 8
Try These:
Ex. Find the roots of each equation by factoring
a.
b. 9
Projectile motion: any object that is thrown or launched into the air typically can be modelled by a quadratic function. 10
Ex. A soccer ball is kicked from ground level with an initial vertical velocity of 32 ft/s. After how many seconds will the ball hit the ground?
11
Try These:
Ex. A football is kicked from ground level with an initial vertical velocity of 48 ft/s. How long is the ball in the air?
12
Ex. Write a quadratic function in standard form with given zeros.
a. 2 and ­1
b.
and ­3
13
Try These:
Ex. Write a quadratic function in standard form with given zeros.
a. 5 and ­5
b.
and 2
14