What represents the vertex and two x-intercepts of y equals x2-2x-35?

Answer 1

(1,-36); -5 and 7

y = x2-2x-35; f(x) = ax2+bx+c

vertex, method 1:

There is a formula for the vertex, if you can remember it. (h,k) = [-b/2a, f(-b/2a)].

-b/2a = 2/2x1 = 2/2 = 1. f(1) = 12-2x1-35 =1-2-35 = -36. The vertex is (1,-36).

vertex, method 2:

Otherwise you complete the square to convert to the vertex form, y = a(x-h)2 + k. Complete the square for x2-2x: the constant term will be (-2/2)2 = (-1)2 = 1.

y = (x2-2x+1)-1-35 = (x-1)2 -36 ==> The vertex is (h,k) = (1,-36).

x-intercepts, method 1:

To find the x-intercepts, let y=0: 0 = x2-2x-35 <=> (x-7)(x+5) = 0 <=> x-7=0 or x+5=0 <=> x=7 or x=-5. The intercepts are -5 and 7.

x-intercepts, method 2:

There is also a nice trick to find the intercepts: 36 = 62. the intercepts are 1+/- 6 = 7 and -5.