# What is the maximum value that the graph of #f(x)= -x^2+8x+7#?

We should know that:

Therefore:

graph{-x^2 + 8x + 7 [-7.88, 12.12, 16.52, 26.52]}

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To find the maximum value of the function ( f(x) = -x^2 + 8x + 7 ), you need to determine the vertex of the parabola represented by the function. The vertex of a parabola in the form ( y = ax^2 + bx + c ) is given by the point ( \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right) ). In this case, ( a = -1 ) and ( b = 8 ). Substituting these values into the vertex formula, you get:

[ x = -\frac{b}{2a} = -\frac{8}{2(-1)} = 4 ]

Substituting ( x = 4 ) into the function, you get:

[ f(4) = -4^2 + 8(4) + 7 = -16 + 32 + 7 = 23 ]

Therefore, the maximum value of the function ( f(x) = -x^2 + 8x + 7 ) is ( 23 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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