Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 5a - Introduction to Quadratic Functions Mini-Lesson Problem 13 WORKED EXAMPLE –APPLICATIONS OF QUADRATIC FUNCTIONS The function h(t) = -16t 2 + 80t + 130, where h(t) is height in feet, models the height of an arrow shot into the sky as a function of time (seconds). Before even LOOKING at the specific questions asked, find the following items and plot/label the graph. 1. Draw an accurate graph of the function using first quadrant values only. Label the x-axis with the input quantity and units. Label the y-axis with the output quantity and units. In this case, I am going to use x[0,10], y[0,250]. You may have to play around with the window to get a good graph. 2. Identify, plot, and label the y-intercept. The y-intercept is (0, 130) since c = 130. 3. Identify, plot, and label the vertex. b 80 The x-coordinate of the vertex is x = 2. 5 . 2 a 2( 16) The y-coordinate is b 2 f ( ) f (2.5) 16(2.5) 80(2.5) 130 230 2a 4. Identify, plot, and label the positive x-intercept – using the process discussed in earlier examples, we want to solve -16t 2 + 80t + 130=0. Using the intersect method, the positive x-intercept is (6.29, 0). QUESTIONS TO ANSWER NOW: a) After how many seconds does the arrow reach its highest point? The x-coordinate of the vertex is 2.5. So, the arrow reaches its highest point after 2.5 seconds. b) How high is the arrow at its highest point? The y-coordinate of the vertex is 230. So, the arrow is 230 ft. at its highest point. c) After how many seconds does the arrow hit the ground? The positive x-intercept is x = 6.29. The arrow will hit the ground after 6.29 seconds. d) What is the practical domain of this function? Time starts at 0 seconds and goes until the arrow hits the ground. So, practical domain is 0 t 6.29 e) What is the practical range of this function? The arrow passes through all height values from 0 (when it hits the ground) to its max height of 230 ft. So, practical range is 0 h ( t) 230 f) What does the y-intercept represent? The y-intercept represents the height of the arrow at time t = 0. Thus, the arrow starts at 130 feet off the ground. Scottsdale Community College Page 194 Intermediate Algebra
Lesson 5a - Introduction to Quadratic Functions Mini-Lesson Problem 14 MEDIA EXAMPLE – APPLICATIONS OF QUADRATIC FUNCTIONS A train tunnel is modeled by the quadratic function h(x) = -0.35x 2 + 25, where x is the distance, in feet, from the center of the tracks and h(x) is the height of the tunnel, also in feet. Assume that the high point of the tunnel is directly in line with the center of the train tracks. a) Draw a complete diagram of this situation. Find and label each of the following: vertex, horizontal intercept (positive side), vertical intercept. b) How wide is the base of the tunnel? c) A train with a flatbed car 6 feet off the ground is carrying a large object that is 15 feet high. How much room will there be between the top of the object and the top of the tunnel? Scottsdale Community College Page 195 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 1b - Linear Equations In the
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Lesson 2b - Functions and Function
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Lesson 6a - Exponents and Rational
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Lesson 6b - Rational Exponents & Ra
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Lesson 6b - Rational Exponents and
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Appendix A: You Try Answers Lesson
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Appendix A: You Try Answers You Try
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Intermediate Algebra – Student Workbook – Second Edition 2013

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