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 ->  Graphs -> 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 231249: 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 texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
We need to come up with the equation of the parabola.
The general equation is:
y=a%28x-p%29%5E2%2Bq
The vertex is (p,q). So in our case, p=-1 and q=2.
The amplitude is a. In our case, it is turned downward, which makes it negative. It has the same width was y=2x^2, so our amplitude is a=-2.
Putting it all together:
y=-2%28x%2B1%29%5E2%2B2
To find the y-intercept, substitute x=0 and solve for y:
y=-2%280%2B1%29%5E2%2B2
y=-2%281%29%5E2%2B2
y=-2%2B2
y=0
The y-intercept is 0.