SOLUTION: find the equation of the parabola with vertex a) ( 2,-12) passing through (0,0) b) (2,6) passing through (0,-6)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: find the equation of the parabola with vertex a) ( 2,-12) passing through (0,0) b) (2,6) passing through (0,-6)      Log On


   

Question 678293: find the equation of the parabola with vertex
a) ( 2,-12) passing through (0,0)
b) (2,6) passing through (0,-6)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a.
vertex( 2,-12), passing through (0,0)
start with vertex form:
y+=+a%28x+-h%29%5E2+%2B+k
then plug in (h,k)=( 2,-12) and (x,y)=(0,0)
0=+a%280+-2%29%5E2+-12
next, solve for a:
0=+a%28-2%29%5E2+-12
0=+4a-12
12=+4a
12%2F4=+a
3+=+a
so
y+=+3%28x+-2%29%5E2-12
y+=+3%28x%5E2-4x%2B4%29-12
y+=+3x%5E2-12x%2B12-12
y+=+3x%5E2-12x

+graph%28+600%2C+600%2C+-10%2C+10%2C+-15%2C+10%2C+3x%5E2+-+12x+%29+


b.

vertex (2,6) passing through (0,-6)
start with vertex form:
y+=+a%28x+-h%29%5E2+%2B+k
then plug in (h,k)=(2,6) and (x,y)=(0,-6)
-6=+a%280+-2%29%5E2+%2B6
next, solve for a:
-6=+a%28-2%29%5E2+%2B6
-6=+4a%2B6
-6-6=+4a
-12%2F4=+a
-3+=+a
so
y+=+-3%28x+-2%29%5E2%2B6
y+=+-3%28x%5E2-4x%2B4%29%2B6
y+=+-3x%5E2%2B12x-12%2B6
y+=+-3x%5E2%2B12x-6
+graph%28+600%2C+600%2C+-10%2C+10%2C+-15%2C+10%2C-3x%5E2%2B12x-6+%29+