Question

I need to find the x coordinate of the vertex of parabola defined by

f(x)= -5x^2 + 9x + 2

Can you please show steps. Thank you

Answer 1

x = -b/2a = -9/-10 = 9/10

To extract it from scratch, complete the square

f(x) = -5x^2 + 9x + 2
= -5(x^2-9/5) + 2
= -5(x^2-9/5 + (9/10)^2) + 2 + 5(9/10)^2
= -5(x - 9/10)^2 + stuff
vertex at x = 9/10

It's just easier to remember that the vertex is at -b/2a

Recall the quadratic formula:

x = -b/2a +/- sqrt(stuff)
This gives the roots, which are equally distant from the vertex, where x = -b/2a.