Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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Chapter 3.8, Problem 52PPS
To determine

To find the area of the triangle that is above the x -axis and below the graph of the function f(x)=|2x|+6 .

Expert Solution & Answer
Check Mark

Answer to Problem 52PPS

  18

Explanation of Solution

Given:

Function: f(x)=|2x|+6

Formula used:

The area bounded by the curve y=f(x) , the x -axis and the ordinate at x=a and x=b is given by:

  x=ax=by=0y=f(x)dydx

Slope of the line

Calculation:

Consider the graph of the function f(x)=|2x|+6=2|x|+6 .

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 3.8, Problem 52PPS

From the graph, it can be observed that the vertex of the function is (0,6) , x -intercepts are -3 and 3.

Since the graph is symmetrical about y -axis, calculate the area on the positive side of x -axis and multiply the result by 2 to get the total area of the triangle.

Slope of the line passing through the points (0,6) and (3,0) :

Slope =m=y2y1x2x1

  =0630=2

Equation of the line passing through the points (0,6) and (3,0) :

  (yy1)=m(xx1)

  (y6)=2(x0)(y6)=2x2x+y=6y=62x

Total area of triangle =2× (area of half triangle)

Now,

Area of half triangle is

  =x=0x=3y=0y=62xdydx=x=0x=3(62x)dx=(6xx2)03=6(3)(3)26(0)+(0)2=189=9

Therefore, total area of triangle that is above the x -axis and below the graph of the function f(x)

  =2× (area of half triangle)

  =2×9=18

Conclusion:

Therefore, the area of the triangle that is above the x -axis and below the graph of the function f(x)=|2x|+6 is 18 .

Chapter 3 Solutions

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Ch. 3.1 - Prob. 2CYUCh. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - Prob. 5CYUCh. 3.1 - Prob. 6CYUCh. 3.1 - Prob. 7CYUCh. 3.1 - Prob. 8CYUCh. 3.1 - Prob. 9CYUCh. 3.1 - Prob. 10CYUCh. 3.1 - Prob. 11CYUCh. 3.1 - Prob. 12CYUCh. 3.1 - Prob. 13PPSCh. 3.1 - Prob. 14PPSCh. 3.1 - Prob. 15PPSCh. 3.1 - Prob. 16PPSCh. 3.1 - Prob. 17PPSCh. 3.1 - Prob. 18PPSCh. 3.1 - Prob. 19PPSCh. 3.1 - Prob. 20PPSCh. 3.1 - Prob. 21PPSCh. 3.1 - Prob. 22PPSCh. 3.1 - Prob. 23PPSCh. 3.1 - Prob. 24PPSCh. 3.1 - Prob. 25PPSCh. 3.1 - Prob. 26PPSCh. 3.1 - Prob. 27PPSCh. 3.1 - Prob. 28PPSCh. 3.1 - Prob. 29PPSCh. 3.1 - Prob. 30PPSCh. 3.1 - Prob. 31PPSCh. 3.1 - Prob. 32PPSCh. 3.1 - Prob. 33PPSCh. 3.1 - Prob. 34PPSCh. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 36PPSCh. 3.1 - Prob. 37PPSCh. 3.1 - Prob. 38PPSCh. 3.1 - Prob. 39PPSCh. 3.1 - Prob. 40PPSCh. 3.1 - Prob. 41PPSCh. 3.1 - Prob. 42PPSCh. 3.1 - Prob. 43PPSCh. 3.1 - Prob. 44PPSCh. 3.1 - Prob. 45PPSCh. 3.1 - Prob. 46PPSCh. 3.1 - Prob. 47PPSCh. 3.1 - Prob. 48PPSCh. 3.1 - Prob. 49PPSCh. 3.1 - 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01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY