May 15, 2015
10.1 Solving Quadratic Equations by Finding Square Roots
Objectives: 1) Evaluate and approximate square roots
2) Solve quadratic equations by finding square roots
Example 1: Evaluate or simplify the expression.
Let's review...
Radical Expressions
Radicand
Perfect Squares
Irrational Numbers
Positive Square Root
Negative Square Root
May 15, 2015
Example 2:
a. Evaluate √b2-4ac when a = 7, b = 8, and c = -1.
b. Evaluate 3 ± 4√6
3
Example 3: Solve the equations.
a. x2 = 6
b. x2 = 144
c. x2 = -7
d. x2 = 50
Example 4: Solve the equation 5x2 - 20 = 0.
STANDARD FORM
for a QUADRATIC EQUATION:
ax2 + bx + c = 0, a≠0
May 15, 2015
10.2 Factoring and Solving Quadratics (a=1)
Objectives: 1) Factor quadratic trinomial expressions.
2) Solve quadratic equations by factoring.
To factor a quadratic expression means to write the expression as a product of linear
expressions. In this lesson we will learn to factor a quadratic expression where a = 1.
STANDARD FORM for a quadratic expression: ax2 + bx + c, a≠0
May 15, 2015
Example 1: Factor (when c is positive).
a) x2 - 16x + 39
b) x2 + 17x + 60
Example 2: Factor (when c is negative).
a) x2 - 12x - 64
b) x2 + 10x - 75
May 15, 2015
Now, let's try solving these equations.
In order to do this we need to use a special property...
ZERO-PRODUCT PROPERTY
Let a and b be real numbers. If ab = 0, then ___________ or ____________.
Example: Solve (x + 7)(x - 12) = 0.
Example 3: Solve.
a) x2 - 16x + 39 = 0
b) x2 + 17x + 60 = 0
c) x2 - 12x - 64 = 0
d) x2 + 10x - 75 = 0