Question

Find the equation of the axis of symmetry of the following parabola algebraically.
y=-x^2+8x

Answer 1

x = 4

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 ...

• a=-1
• b=8
• c=0

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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.