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WARM UP What do you remember?...
QUADRATIC EQUATIONSSECTION 5.5
OBJECTIVES
By the end of this part of the lesson, you should be able to…
• Simplify square roots.
• Solve quadratic equations by finding square roots.
SOLVING QUADRATIC EQUATIONSWITH SQUARE ROOTS
02 cax
If a quadratic equation is missing the b term we can solve using square roots.
The goal is to get x by itself .
EXAMPLE 1: SIMPLIFYING RADICALS
24.
49
81.
45.
c
b
a
EXAMPLE 2: SIMPLIFYING RADICALS
121
27.
10.
32.
c
b
a
EXAMPLE 4: SOLVING BY FINDING SQUARE ROOTS
5x 2 1800
Step 1) Rewrite in form ax2 = c.
Step 2) Isolate x2.
Step 3) Simplify.
Step 4) Take the square root of each side.
EXAMPLE 5: SOLVING BY FINDING SQUARE ROOTS
EXAMPLE 6: SOLVING BY FINDING SQUARE ROOTS
4x 2 250
EXAMPLE 6: SOLVING BY FINDING SQUARE ROOTS
OBJECTIVES
By the end of today, you should be able to…
• Solve quadratic equations by factoring and graphing.
What does it mean to solve an equation?
Quick Review:When you solve an equation, you’re finding the values that make the statement true.
QUADRATIC EQUATIONS
Remember - the standard form of a quadratic equation is ax2 + bx + c = 0, where a ≠ 0.
You can solve some quadratic equations in standard form by factoring the quadratic expression and then using…
The Zero-Product Property!
THE ZERO-PRODUCT PROPERTY
The Zero-Product Property helps us solve quadratic equations that have been factored.
The Zero-Product Property states:If ab = 0, then a = 0 or b = 0.
For example, if (x + 3)(x - 7)=0, then (x + 3) = 0 or (x - 7) = 0.
EXAMPLE 1: SOLVING BY FACTORING
Solve by factoring.Step 1) Write in standard form.
Step 2) Factor.
Step 3) Use the Zero-Product Property.
Step 4) Solve for x.
EXAMPLE 2: SOLVING BY FACTORING
Solve by factoring.Step 1) Write in standard form.
Step 2) Factor.
Step 3) Use the Zero-Product Property.
Step 4) Solve for x.
EXAMPLE 3: SOLVING BY FACTORING
Solve by factoring.Step 1) Write in standard form.
Step 2) Factor.
Step 3) Use the Zero-Product Property.
Step 4) Solve for x.
EXAMPLE 4: SOLVING BY FACTORING
Solve by factoring.Step 1) Write in standard form.
Step 2) Factor.
???
SOLVING BY GRAPHING
You can solve a quadratic equation in standard form by graphing its related quadratic function,
y = ax2 + bx +c and finding the x-intercepts.
Quadratic equation cannot
be solved by factoring
Quadratic equation can be solved by graphing!
SOLVING BY GRAPHING
1)Write in standard form2)Graph in your calculator3)Find the x-intercepts
SOLVING BY GRAPHING
Equation X-intercept(s)
x2 – 6x + 9
x2 + 4x – 5
HOMEWORK
Worksheet 5.5 #s 1, 3, 7, 11, 30, 34, 53, 60
Systems Projects – due Monday!
