SOLUTION: what quadratic function represents a porabola where the graph has vertex at (-4,2) and passes through (3,9)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: what quadratic function represents a porabola where the graph has vertex at (-4,2) and passes through (3,9)      Log On


   

Question 75527: what quadratic function represents a porabola where the graph has vertex at (-4,2) and passes through (3,9)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Using this general equation:
y=a%28x-h%29%5E2%2Bk where a is the compression/stretch factor and (h,k) is the vertex. So the equation comes to:
y=a%28x-%28-4%29%29%5E2%2B2
y=a%28x%2B4%29%5E2%2B2
y=a%28x%5E2%2B8x%2B16%29%2B2 foil the squared parenthesis
y=ax%5E2%2B8ax%2B16a%2B2 distribute the a
Now plug in the point (3,9)
9=a%283%29%5E2%2B8%283%29a%2B16a%2B2
9=9a%2B24a%2B16a%2B2
9=49a%2B2
7=49aSubtract 2 from both sides
a=1%2F7 Divide both sides by 49
So the equation is
y=%281%2F7%29%28x%2B4%29%5E2%2B2
Check:
Plug in (3,9) to see if it works
9=%281%2F7%29%283%2B4%29%5E2%2B2
9=%281%2F7%29%287%29%5E2%2B2
9=%281%2F7%2949%2B2
9=7%2B2
9=9 works