Download B. Quadratic Formula

MAC 1105 - Section 3.2b
Solving Quadratic Equations Using the Quadratic Formula
A. Skill Review
1. Simplify the following radical expressions
a.
50
b.
c. 3 72
200
d. 5 120
2. Simplify the following fractional expressions
a.
6  12 5
3
b.
 10  4 6
6
c.
14  2 3
7
d.
6  12
3
3. Use your calculator to calculate rounded decimal values for parts a and c of item 2 above.
a.
c.
B. Quadratic Formula
A Quadratic equation in the form ax2 + bx + c = 0 can be solved symbolically by substituting the
values for a, b and c into the Quadratic Formula:
 b  b 2  4ac
2a
Where the value of b 2  4ac is know as the discriminant. (NOTE: There is a typographical error in
the text on pg 185 which lists the discriminant as b 2  4ac )
x
The answers may be given in simplified radical form (representing EXACT answers) or may be
entered into the calculator and rounded to the nearest hundredth.
Use the quadratic formula to solve the following equations. Give both exact answers and rounded
decimal values.
1. x2 + 5x – 2 = 0
2. 2x2 + 4x - 7 = 0
3. -2x2 + 7x = 3
4. x2 = 3(x – 2)
C. Application: Graphing Quadratic Functions
To sketch the graph of a quadratic function that “does not factor”, first determine the vertex
using the vertex formula. Then use the quadratic formula to determine exact values for the xintercepts. Convert these values to decimals. Sketch the graph, labeling the vertex and the xintercepts.
Example:
1. f(x) = 2x2 + 4x – 7
(see problem B2 on the front.)
2. You Try: f(x) = x2 – 6x + 3
**NOTE: Extra practice on solving all types of Quadratic Equations can be found
via the class assignments sheet.
Homework: SOLVE THE FOLLOWING PROBLEMS USING THE QUADRATIC FORMULA
METHOD (NOT COMPLETING THE SQUARE). GIVE YOUR ANSWERS IN SIMPLIFIED RADICAL
FORM. Problems 65 – 71 odd, 75, 77
Also, given the following functions, determine the vertex and x-intercepts to the nearest hundredth
and sketch a graph:
1. f(x) = 2x2 – 8x + 1
Worksheet answers: 1) v = (2, -7) Int = .13 and 3.87
2. f(x) = -x2 + 2x + 5
2) v=(1,6) int = -1.45 and 3.45
(054)