The maximum value of y in the equation y = -x2 + 6x – 8 is y=

  1

Step-by-step explanation:

A graph shows you very quickly that the maximum value of y is 1.

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There are several ways to get there algebraically. The axis of symmetry is given for ax^2 +bx by x=-b/(2a). Here, that value is x=(-6)/(2(-1)) = 3. The maximum y-value will correspond to this x-value:

  y = -3² +6·3 -8 = -9 +18 -8 = 1

The maximum value of y is 1.

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The axis of symmetry can also be found by factoring:

  y = -(x -4)(x -2)

It is halfway between the values of x that make these factors zero, so is ...

  x=(4+2)/2 = 3

For that value of x, we find y to be ...

  y = -(3 -4)(3 -2) = 1

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We can also rearrange the equation to vertex form:

  y = -(x^2 -6x) -8

  = -(x^2 -6x +9) -8 -(-9)

  = -(x -3)^2 +1

The vertex is (3, 1), so the maximum value of y is 1.