4
EXAMPLE
Choose a Solution Method
The path followed by a penguin leaping out of the water is given
by h 0.05x2 1.178x, where h is the vertical height (in feet) of the
penguin above the water and x is the horizontal distance (in feet) traveled over
the water. Find the horizontal distance traveled by this penguin when it reaches
a vertical height of 6 feet.
PENGUINS
h
x
Solution
To find the horizontal distance when h 6, solve the quadratic equation
6 0.05x2 1.178x. This equation cannot be factored easily and cannot be
solved easily by completing the square. The quadratic formula is a good choice.
b b2
4ac
2a
Write quadratic formula.
x 1.178 1.1
782
4(
0.0
5)(
6)
2(0.05)
Substitute values for a, b, and c.
x ≈ 7.4
Use a calculator.
x ANSWER 䊳
or
x ≈ 16.1
The penguin reaches a vertical height of 6 feet at horizontal
distances of about 7.4 feet and about 16.1 feet. Check these solutions
in the original equation.
Choose a Solution Method
Choose a method and solve the quadratic equation. Explain your choice.
8. x2 3 0
9. 2x2 8
10. x2 3x 4 6
You have learned the following five methods for solving quadratic equations.
SUMMARY
Methods for Solving Quadratic Equations
Method
Comments
FINDING SQUARE ROOTS
Efficient way to solve ax 2 c 0.
(Lesson 9.2)
GRAPHING
(Lesson 9.5)
USING THE QUADRATIC
FORMULA
Can be used for any quadratic equation.
(Lesson 9.6)
FACTORING
(Lesson 10.5–10.8)
COMPLETING THE SQUARE
(Lesson 12.5)
718
Can be used for any quadratic equation. Enables you to
approximate solutions.
Chapter 12
Efficient way to solve a quadratic equation if the quadratic
expression can be factored easily.
Can be used for any quadratic equation, but is best suited for
quadratic equations where a 1 and b is an even number.
Radicals and More Connections to Geometry