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Example 1: Determine the maximum or minimum of the equation y=-4x² +24x - 35

Example 1: Determine the maximum or minimum of the equation y=-4x² +24x - 35

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I || 3 11 = = 3 = = b 20 24 -8 Therefore, the x-value of the vertex is 3. Next, substitute this value into the original equation to find the corresponding y-value. 24 2(-4) 1 x-value of the vertex Substitute in a = -4 and b = 24 Simplify -4² +24-35 Substitute x3 -4(3)² +24(3)-35 Simplify -36+72-35 The vertex is (3, 1). Therefore, the maximum y-value is 1, which occurs where x = 3 as illustrated below: y Maximum y-value H X
Transcribed Image Text:I || 3 11 = = 3 = = b 20 24 -8 Therefore, the x-value of the vertex is 3. Next, substitute this value into the original equation to find the corresponding y-value. 24 2(-4) 1 x-value of the vertex Substitute in a = -4 and b = 24 Simplify -4² +24-35 Substitute x3 -4(3)² +24(3)-35 Simplify -36+72-35 The vertex is (3, 1). Therefore, the maximum y-value is 1, which occurs where x = 3 as illustrated below: y Maximum y-value H X
If the leading coefficient a is positive, then the parabola opens upward, and there will be a minimum y-value. If the leading coefficient a is negative, then the parabola opens downward and there will be a maximum y-value. Line of Symmetry Parabola yax² +bx+c a <0 20 a>0 To find these important points given a quadratic function, we use the vertex. The line of symmetry is the vertical line used to find the x-value of the vertex. opens upward opens downward Example 1: Determine the maximum or minimum of the equation y = -4x² +24x - 35 Solution: Because a = 4, we know that the parabola opens downward and there will be a maximum y-value. To find it, first find the x-value of the vertex.
Transcribed Image Text:If the leading coefficient a is positive, then the parabola opens upward, and there will be a minimum y-value. If the leading coefficient a is negative, then the parabola opens downward and there will be a maximum y-value. Line of Symmetry Parabola yax² +bx+c a <0 20 a>0 To find these important points given a quadratic function, we use the vertex. The line of symmetry is the vertical line used to find the x-value of the vertex. opens upward opens downward Example 1: Determine the maximum or minimum of the equation y = -4x² +24x - 35 Solution: Because a = 4, we know that the parabola opens downward and there will be a maximum y-value. To find it, first find the x-value of the vertex.
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