Chapter 5 Quadratic Functions - 5.6 The Quadratic Formula And The Discriminant Worksheet Template
ADVERTISEMENT
1
2
3
4
5
6
7
8Page 1 of 2
5.6
The Quadratic Formula and the
Discriminant
GOAL
1
S
E
Q
F
OLVING
QUATIONS WITH THE
UADRATIC
ORMULA
What
you should learn
GOAL
Solve quadratic
1
In Lesson 5.5 you solved quadratic equations by completing the square for
equations using the quadratic
each equation separately. By completing the square once for the general equation
formula.
2
ax
+ bx + c = 0, you can develop a formula that gives the solutions of any
quadratic equation. The formula for the solutions is called the
quadratic formula.
Use the quadratic
GOAL
2
A derivation of the quadratic formula appears on page 895.
formula in real-life situations,
such as baton twirling in
Example 5.
T H E Q UA D R AT I C F O R M U L A
Why
you should learn it
Let a, b, and c be real numbers such that a ≠ 0. The solutions of the
To solve real-life
2
quadratic equation ax
+ bx + c = 0 are:
problems, such as finding the
2
ºb ±
b
º 4 a c
speed and duration of a thrill
x =
2a
ride in Ex. 84.
Remember that before you apply the quadratic formula to a quadratic equation, you
2
must write the equation in standard form, ax
+ bx + c = 0.
Solving a Quadratic Equation with Two Real Solutions
E X A M P L E 1
2
Solve 2x
+ x = 5.
S
OLUTION
2
2x
+ x = 5
Write original equation.
2
2x
+ x º 5 = 0
Write in standard form.
2
ºb
±
b
º 4
a
c
x =
Quadratic formula
2a
2
º1
±
1
º 4
(2
)(
º 5
)
x =
a = 2, b = 1, c = º5
2 (
)
2
º1 ± 4 1
x =
Simplify.
4
The solutions are
º1 +
4 1
x =
≈ 1.35
4
and
º1 º 4 1
x =
≈ º1.85.
4
Zero
X=1.3507811 Y=0
2
Graph y = 2x
+ x º 5 and note that
CHECK
the x-intercepts are about 1.35 and about º1.85.
5.6 The Quadratic Formula and the Discriminant
291
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education