I||311== 3==b2024-8Therefore, the x-value of the vertex is 3. Next, substitute this value into the originalequation to find the corresponding y-value.242(-4)1x-value of the vertexSubstitute in a = -4 and b = 24Simplify-4² +24-35 Substitute x3-4(3)² +24(3)-35 Simplify-36+72-35The vertex is (3, 1). Therefore, the maximum y-value is 1, which occurs where x = 3 asillustrated below:yMaximum y-valueHX If the leading coefficient a is positive, then the parabola opens upward, and there will be aminimum y-value. If the leading coefficient a is negative, then the parabola opensdownward and there will be a maximum y-value.Line of SymmetryParabola yax² +bx+ca <020a>0To find these important points given a quadratic function, we use the vertex. The line ofsymmetry is the vertical line used to find the x-value of the vertex.opens upward opens downwardExample 1: Determine the maximum or minimum of the equationy = -4x² +24x - 35Solution: Because a = 4, we know that the parabola opens downward and there will be amaximum y-value. To find it, first find the x-value of the vertex.

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Answered: Example 1: Determine the maximum or…

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

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.1: Quadratic Functions

Problem 73E: Height of a football A football is thrown by a quarterback from the 10-yard line and caught by the...

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Question

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.

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