1. Solving Quadratic Equations.
Factoring to Solve Quadratic Equations
What you’ll learn
To solve quadratic equations by graphing and
using square roots.
To solve quadratic equations by factoring.
Vocabulary
Quadratic equation,
Standard form of a quadratic equation,
Zero of a function,
Zero product property.

2.  Take a note: A quadratic equation is an equation that
can be written in the form
This form is called the standard form of a quadratic
equation.
The solution of a quadratic equation and the
x-intercepts of the graph of the related function
are often called roots of the equation or zeros of the
function. (x-intercept meaning when the y=0) 

3. Problem 1: Solving by graphing
What are the solutions of each equation?
Graph

4. Problem 2: Solving using the square root.
What are the solutions of ?
Isolate the x in one side
Find the square root of each
side and simplify
Your turn:
Answers

5. V=l.w.h w l h=3ft Problem 3: An aquarium is designing a new exhibit to
showcase tropical fish. The exhibit will include a tank
that is rectangular prism with length l that is twice
the with w. The volume of the tank is 420 cubic ft.
What is the width of the tank to the nearest foot? w
Answer
V=l.w.h
h=3ft l
The tank cannot be a
negative width so only
the positive root make sense.
The tank will have a width of 8.4 ft

6. Your turn: Suppose the tank in problem 3 will have
a height of 4 ft. and a volume of 500 cubic feet.
What is the width of the tank to the nearest tenth
of a foot?
Answer:
7.9 ft.

7. Problem 4: Using the Zero Property after factoring.
What are the solutions of the equation?
Factor
Zero Property
Solve it
Your turn
Answer

8. Problem 5: Writing the Standard Form First.
What are the solutions of ?
Make the equation =0
Factor
Zero Property
Solve for x
Your turn
Answer -7

9. Problem 6: Using Factoring to Solve a Real World Problem
You are constructing a frame for the rectangular photo shown.
You want the frame to be the same width all
the way around and the total area of the
frame and photo to be 315 sq. in. What
should the outer dimensions of the
frame be? x x x
11in
Substitute
17 in
Make equation
equals to zero x
GCF: 4
Reasonable solution
is x=2
Factor
Solve for x

10. HOME
From the text book go to page 559 and in a
piece of paper do exercises
Show me the work!!!!!!

11. Classwork odd Homework even
TB pgs exercises 8-54
pgs exercises 8-41