A2 5.3 Zeros of a function- any number

Zeros of a function- any number (r) that make f(x)=0

*distributing factors is like driving a car backwards

ZERO PRODUCT PROPERTY-

if p*q=0, then p=0 or q=o



EX 12: solve the following equation for x
x^2+5x+6=0 check:
(x+2)(x+3)=0 (-2)^2+5(-2)+6
*solve for x 4-10+6+0 (correct)
(x+2)=0, or (x+3)=0 check:
x can equal: (-3)^2+5(-2)+6
x=-2, or x=-3 9-15+6=0 (correct)

CAN'T SOLVE QUADRATIC EQUATIONS LIKE LINEAR EQUATIONS:
*5x+7=0
5x=-7
x=-7/5
when the y equals 0, we typically get one solution in linear equations because it only crosses the x axis once

*x^2+5x+6=0
(have to use factoring, can't solve it like the equation above)
when the y equals 0, we get TWO solutions for quadratic equations because the parabola crosses the x axis twice
EX 13: solve for x: 2x^2-11x=0
x(2x-11)=0
^ ^
p q
x=0, or x+11/2

*the box method does not work if you can factor out each term*

EX 14: solve 4x^2-24x+36=0
4(x^2-6x+9)=0
(now guess and check)
4(x-3)(x-3)=0
x=3, or x=3 (accept a parabola can't cross the x axis twice)
if the vertex lies on the x axis, you only have one zero

example <---

for quiz tomorrow: know how to factor, and know how to solve using zeros product property, and difference of squares

Oakley is now confused Oakley is trying to figure something out right now that he doesn't understand Oakley kind of sees how it works now, but is still somewhat dumbfound
Now Oakley is going to FOIL and check it
Oakley just said good job, because he foiled it and it worked

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