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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.
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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!
3
Ex. Find the zeros of by using a graph and table.
4
Try These:
Ex. Find the zeros of by using a graph and a table.
5
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.
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Ex. Find the zeros of each function by factoring.
a.
b.
7
Try These:
Ex. Find the zeros of each function by factoring.
a.
b.
8
Ex. Find the roots of each equation by factoring.
a.
b.
9
Try These:
Ex. Find the roots of each equation by factoring
a.
b.
10
Projectile motion: any object that is thrown or launched into the air typically can be modelled by a quadratic function.
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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?
12
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?
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Ex. Write a quadratic function in standard form with given zeros.
a. 2 and 1
b. and 3
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Try These:
Ex. Write a quadratic function in standard form with given zeros.
a. 5 and 5
b. and 2