Solving Quadratic Equations By Using The Quadratic Formula Worksheet With Answers Page 24
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419-5 Solving Quadratic Equations by Using the Quadratic Formula
The discriminant is 18.25.
Since the discriminant is positive, the equation has two real solutions.
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41. CCSS MODELING The percent of U.S. households with high-speed Internet h can be estimated by h = −0.2n
+
7.2n + 1.5, where n is the number of years since 1990.
a. Use the Quadratic Formula to determine when 20% of the population will have high-speed Internet.
b. Is a quadratic equation a good model for this information? Explain.
SOLUTION:
a.
Write the equation in standard form.
For this equation, a = –0.2, b = 7.2, and c = –18.5.
Since n is the number of years since 1990 add the solutions to 1990.
1990 + 3 = 1993; 1990 + 33 = 2023
b.
A quadratic equation not a good model for this information. The parabola has a maximum at about 66, meaning
only 66% of the population would ever have high-speed Internet.
[-3. 48] scl: 5, by [-2, 68] scl: 7
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42. TRAFFIC The equation d = 0.05v
+ 1.1v models the distance d in feet it takes a car traveling at a speed of v miles
per hour to come to a complete stop. If Hannah’s car stopped after 250 feet on a highway with a speed limit of 65
miles per hour, was she speeding? Explain your reasoning.
SOLUTION:
Write the equation in standard form.
For this equation, a = 0.05, b = 1.1, and c = –250.
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