1. Factoring Quadratic Expressions. Quadratic Equations
What you’ll learn
To factor polynomial expressions.
To solve quadratic equations by factoring.
To solve quadratic equations by graphing.
Vocabulary
Factoring, GCF, perfect square trinomial
difference of two squares, zero of a
function, zero product property.

2. Take a note
What is a factoring? Factors of a given number are
numbers that have a product equal to the given
number. Factors of a given expressions that have
a product equal to the given expression. Factoring is
rewriting an expression as a product of its factors.
GFC the greatest common factor
of an expression is a common factor of
the terms in the expression. Is the
common factor with the greatest
coefficients and the greatest exponents
You can factor any expression that the
GCF not equal to one.

3. Problem 1: Factoring when
Answer A:
Factors of ,20 2, ,5
Sum of factors
Answer B:
Factors of , ,36 -3,24 -4,18 -6, ,9
Sum of factors
Answer C: First factor out -1 so
Factors of , , ,-4
Sum of factors

4. Your turn
What is the expression in factored form?
Answers:

5. Problem 2 Finding common factors
What is the expression factored from?
Get GCF=3 and the variable with the least exponent
The GCF=4 and then do the factorization
Your turn
What is the expression factored from?

6. Problem 3 Factoring when
What is the expression of the factored form?
I can not simplify the whole expression
Then multiply a times c
Then factor ,24 2,12 3,8 4,6
Sum of factors
Rewrite the expression using
b=3+8
Group them and find common factor

7. Your turn
What is the expression in the factored form of?
Can you factor this expression into
a product of two binomials? Explain
No, there is no factors of a and c whose product
is 1 and whose sum is 1.

8. Your turn again
What is the expression in a factored form of ?
Another way to do it is by verifying that

9. Take a note
When this happen you are factoring a perfect square
trinomial. If ax²+bx+c is a perfect square trinomial,
then ax² and c are squares of the binomial and thus
are both positive. bx is twice the product of the
terms of the binomial. If b is negative then the
binomial terms have opposite signs.
The expression a²-b²is the
difference of two squares There is a pattern
of factors(a-b)(a+b)

10. Your turn again
What are the factors of?

11. Quadratic Equations
Take a note
Wherever the graph of a function f(x) intersects the
x-axis, f(x)=0. A value of x for which f(x)=0 is a
zero of the function.
To find the zeros of a quadratic function y=ax²+bx+c
Solve the related quadratic function by factoring and
make the equation 0=ax²+bx+c
You can solve some quadratic equations in standard form by factoring the quadratic expression using the zero product property.
If ab=0 then a=0 or b=0

12. Problem 4:
Solving a quadratic equation by factoring
What are the solutions of the quadratic equation
Factor the quadratic equation
Use the zero product property
The solutions are x=2 and x=3
If you are graphing this points will be
(2,0) and (3,0)

13. Problem 5 385 ft. 74 ft. c)Domain: 0 ≤ x ≤ 385 Answer:
The function f (x) = x² x models the path of a baseball, where f (x) gives the height of the ball and x gives the distance from where it is hit in feet.
a. How far does the ball travel before hitting the ground?
b. How high does the ball go?
c. What is a reasonable domain and range for such a function?
385 ft.
74 ft.
c)Domain: 0 ≤ x ≤ 385
Range: 0 ≤ y ≤ 74
Answer:
395

14. c)domain: 0 ≤ x ≤ 21 and range: 0 ≤ x ≤ 3
Your turn
From the time Mark Twain wrote The Celebrated Jumping Frog of Calaveras County in 1865, frog jumping competitions have been growing in popularity. The graph shows a function modeling the height of frog’s jump, where x is the distance, in feet, from the jump’s start.
a)How far the frog jump? b) How high the frog jump?
c)What is the reasonable domain and range for such a frog-jumping function?
a) the frog jump about ft.
Answer
b) y=-0.029(10.17)²+0.59(10.17)≈3.0
c)domain: 0 ≤ x ≤ 21 and range: 0 ≤ x ≤ 3

15. Classwork odd Homework even
Text book pages exercises 14-90
Text book pages exercises 9-59