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The shaded region shown below is bounded by the functions f (x) = -4x2 + 10 and g(x) = x + 6 and the x and y axes. Find the area of the shaded region using a calculator, rounding to the nearest thousandth. 12

The shaded region shown below is bounded by the functions f (x) = -4x2 + 10 and g(x) = x + 6 and the x and y axes. Find the area of the shaded region using a calculator, rounding to the nearest thousandth. 12

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section: Chapter Questions
Problem 25MCQ
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The image contains a mathematical problem and graph related to finding the area of a shaded region. ### Problem Statement: The shaded region shown below is bounded by the functions \( f(x) = -4x^2 + 10 \) and \( g(x) = x + 6 \) and the \( x \) and \( y \) axes. Find the area of the shaded region using a calculator, rounding to the nearest thousandth. ### Graph Description: - The coordinate plane is labeled with \( x \) and \( y \) axes. - The parabola \( f(x) = -4x^2 + 10 \) opens downward, intersecting the \( y \)-axis at \( y = 10 \). - The line \( g(x) = x + 6 \) is a straight line with a positive slope, intersecting the \( y \)-axis at \( y = 6 \). - The shaded region is located between the parabola and the line, extending from the \( y \)-axis to the points approximately at \( x = 1 \) and \( x = 2 \). ### Graph Details: - The two curves intersect at two points, defining the limits for the shaded area on the \( x \)-axis. - The region in question appears to be below the line \( g(x) \) and above the curve \( f(x) \), filling a space that includes the \( y \)-axis.
Transcribed Image Text:The image contains a mathematical problem and graph related to finding the area of a shaded region. ### Problem Statement: The shaded region shown below is bounded by the functions \( f(x) = -4x^2 + 10 \) and \( g(x) = x + 6 \) and the \( x \) and \( y \) axes. Find the area of the shaded region using a calculator, rounding to the nearest thousandth. ### Graph Description: - The coordinate plane is labeled with \( x \) and \( y \) axes. - The parabola \( f(x) = -4x^2 + 10 \) opens downward, intersecting the \( y \)-axis at \( y = 10 \). - The line \( g(x) = x + 6 \) is a straight line with a positive slope, intersecting the \( y \)-axis at \( y = 6 \). - The shaded region is located between the parabola and the line, extending from the \( y \)-axis to the points approximately at \( x = 1 \) and \( x = 2 \). ### Graph Details: - The two curves intersect at two points, defining the limits for the shaded area on the \( x \)-axis. - The region in question appears to be below the line \( g(x) \) and above the curve \( f(x) \), filling a space that includes the \( y \)-axis.
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