SOLUTION: find the y-intercept of a parabola whose vertex is (-1,2), which is turned downward, and whose width is the same as y=2x^2.

Algebra ->  Equations -> SOLUTION: find the y-intercept of a parabola whose vertex is (-1,2), which is turned downward, and whose width is the same as y=2x^2.      Log On


   

Question 230804: find the y-intercept of a parabola whose vertex is (-1,2), which is turned downward, and whose width is the same as y=2x^2.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
find the y-intercept of a parabola whose vertex is (-1,2), which is turned
downward, and whose width is the same as y = 2x^2.
:
Using the form ax^2 - bx + c = y
:
We know the axis of symmetry; x = -1, and a=2
:
use the axis of symmetry formula to find b; x = -b/(2*a)
-1 = %28-b%29%2F%282%2A2%29
-1 = %28-b%29%2F4
4(-1) = -b
-4 = -b
b = +4
:
We have 2x^2 + 4x + c = y
:
when x=-1, y=2
2(-1)^2 + 4(-1) + c = 2
2(1) - 4 + c = 2
2 - 4 + c = 2
-2 + c = 2
c = 2 + 2
c = 4
:
equation: y = 2x^2 + 4x + 4; therefore, the y intercept = 4
:
looks like this:
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+2x%5E2%2B4x%2B4%29%29+
Vertex -1,2; y intercept +4