Math Problem Statement
The figure shows the graph of y equals negative ax squared plus bx plus c. Suppose that the points left parenthesis negative h comma y 0 right parenthesis comma left parenthesis 0 comma y 1 right parenthesis comma and left parenthesis h comma y 2 right parenthesis are on the graph. The area enclosed by the parabola, the x-axis, and the lines x equals negative h and x equals h may be given by the formula below. Find the area enclosed by f left parenthesis x right parenthesis equals negative 6 x squared plus 7 comma the x-axis, and the lines xequalsminus1 and xequals1. AreaequalsStartFraction h Over 3 EndFraction left parenthesis y 0 plus 4 y 1 plus y 2 right parenthesis x y left parenthesis negative h comma y 0 right parenthesisleft parenthesis 0 comma y 1 right parenthesisleft parenthesis h comma y 2 right parenthesis
A coordinate system has a horizontal x-axis and a vertical y-axis. A parabola opens downward from the plotted point (0, y 1) and passes through the plotted points (negative h, y 0) and (h, y 2). Question content area bottom Part 1 The area is
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Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Area under Curves
Formulas
Quadratic function: f(x) = ax^2 + bx + c
Area formula: Area = (h/3) * (y0 + 4y1 + y2)
Theorems
Parabolic Area Formula
Suitable Grade Level
Grades 10-12
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