Question

Show that the line of symmetry for the graph of f(x)=(x-a)(x-b) is x=(a+b)/2, where a and b are any positive real numbers.

I really have no clue to do it. Please help!!!!THANKS A LOT!

Answer 1

This is the quadratic function. The graph of this function is a parabola, parallel to the y axis, with roots at the points (a,0) and (b,0). It follows that the line of symmetry is parallel to the y-axis and passes through a point half way between the two roots, which would be (a+b)/2.