Answer:
x = 4
Step-by-step explanation:
The x-coordinate of the vertex of standard form quadratic y=ax²+bx+c is given by x=-b/(2a). This is also the equation of the axis of symmetry, the vertical line through the vertex.
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coefficients
The given equation is ...
y = -x^2 +8x
Comparing this to the standard form quadratic expression, we see that ...
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equation
Using these values in the equation of the axis of symmetry, we get ...
x = -8/(2(-1)) = 8/2 = 4
Th equation of the axis of symmetry is x=4.
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Additional comment
The x-coordinate of the vertex is also found as the midpoint of the two x-intercepts. Those are the values of x that make y=0:
0 = -x² +8x
0 = -x(x -8)
The factors are zero when x=0 and x=8, so the midpoint between them is ...
x = (0 +8)/2 = 4
The axis of symmetry is x=4.
