Question

For my parabola assignment: what is the relationship between the x-intercepts and the x coordinate of the turning point? :) :) PLEASE HELP

Answer 1

the line of symmetry is in the middle of the x - intercepts... the turning point occurs on the line of symmetry....

e...g. y = x^2 + x - 6

has x intercepts at x = -3 & 2 line of symmetry is x = -b/2a so x = -1/2

midpoint of -3 and 2 = -1/2

Using the 1st derivative to find the stationary point..

y' = 2x + 1

stationary point at x = -1/2