Question

The x-intercepts of a parabola are 5 and -7.

What is the equation of the axis of symmetry?

a) x = 12

b) x = - 1

c) x= -2

d) x = 1

e) x =2

Answer 1

b) x = - 1

Explanation:

You want the equation of the axis of symmetry for a parabola with x-intercepts of 5 and -7.

Symmetry

The given x-intercepts are symmetrical about the axis of symmetry, so its x-intercept is the midpoint of the segment between (5, 0) and (-7, 0).

That midpoint is ...

((5, 0) +(-7, 0))/2 = (-2, 0)/2 = (-1, 0)

The vertical line through this point has equation ...

x = -1