Kian is driving 48 miles per hour and is starting to merge onto the highway; therefore, he must increase his speed. He gradually accelerates at a rate of 7 miles per hour for several seconds. a. Substitute the initial velocity and constant acceleration into the formula to write an equation to represent the distance Kian travels. b. Use the Quadratic Formula to determine the roots of the equation. What do the roots represent in the context of the problem situation? Explain your reasoning.
Kian is driving 48 miles per hour and is starting to merge onto the highway; therefore, he must increase his speed. He gradually accelerates at a rate of 7 miles per hour for several seconds. a. Substitute the initial velocity and constant acceleration into the formula to write an equation to represent the distance Kian travels. b. Use the Quadratic Formula to determine the roots of the equation. What do the roots represent in the context of the problem situation? Explain your reasoning.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.5: Solving Quadratic Equations By Completing The Square
Problem 41PPS
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Kian is driving 48 miles per hour and is starting to merge onto the highway; therefore, he must increase his speed. He gradually accelerates at a rate of 7 miles per hour for several seconds.
a. Substitute the initial velocity and constant acceleration into the formula to write an equation to
represent the distance Kian travels.
b. Use the Quadratic Formula to determine the roots of the equation. What do the roots represent in
the context of the problem situation? Explain your reasoning.
Transcribed Image Text:system of equations.
Tuu cun sulve quadratic equations using factoring, completing the
square, the Quadratic Formula, and graphing.
Practice
1. Solve each equation.
a. 0 = x² – 7x - 18
C. 0 = x² – 10x + 12
e. 3x2 – 22x +7 = 0
b. x2 + 10x = 39
d. 2x2 + 4x = 0
2. Determine the roots of each equation. Check your solutions.
a. y = x² + 9x + 3
b. y = 3x2 + 24x - 6
3. Kian is driving 48 miles per hour and is speeding up to merge onto the highway. He gradually
accelerates at a rate of 7 miles per hour for several seconds. The formula s = ut +at? can be used
to calculate the distance, s, an object travels in t seconds. In this formula, u represents the initial
velocity, and a represents a constant acceleration.
a. Substitute the initial velocity and constant acceleration into the formula to write an equation to
represent the distance Kian travels.
b. Use the Quadratic Formula to determine the roots of the equation. What do the roots represe
the context of the problem situation? Explain your reasoning.
4. Determine the solution to each system of equations
a.( y = x2 - 4x - 8
ly = -x² – 10x + 12
b. [y = 2x2 + 3x - 2
ly = -2x2 + 7x -3
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