Answer:
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.
