Y = 2x^2 - 4x - 6
a.) convert to vertex form
b.) find x- intercept. Solutions must be exact
c.) find all values such that y > 0
d.) find the range of dunction
e.) when is the function decreasing?
+36915 1
2 (x^2-2x) -6 complete the square
Y= 2 (x-1)^2 - 8
2
x intercept(s) happen when y = 0 set the equation to y=0
0 = 2(x-1)^2 - 8
4 = (x-1)^2
+- 2 = x-1
x = 3, -1
3
From 2 above (-inf,-1) U (3, +inf)
Range = all values of x are allowed in the domain...the range extends from the vertex at -8 to + inf [-8, +inf)
This is an upright parabola....the funtion is decreasing from -inf to the vertex (1,-8) or for values of x ( -inf ,1]
