SOLUTION: equation of the parabola with vertex (-6,2)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: equation of the parabola with vertex (-6,2)      Log On


   

Question 698163: equation of the parabola with vertex (-6,2)
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use the vertex form:



where is the vertex.





where . Note that the equation is for a set of parabolas with infinite elements; one for each possible value of

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the equation for a parabola can also be written in "vertex form":
y+=+a%28x+-h%29%5E2+%2B+k
In this equation, the vertex of the parabola is the point (h, k).

if (h, k)=(-6, 2), than

y+=+a%28x-%28-5%29%29%5E2+%2B+2

y+=+a%28x+%2B5%29%5E2+%2B+2.........the coefficient of x here is -2ah
y+=+k+%2B+sqrt%28-4h%29... to find the y-intercept, set x+=+0
y+=+2+%2B+sqrt%28-4%28-6%29%29
y+=+2+%2B+sqrt%2824%29
y+=+2+%2B+4.9
y+=+6.9

next, we find a

x+=+h+%2B+k%5E2%2F4a+

x+=+-6+%2B+2%5E2%2F4a
x+=a-6.......since y+=+6.9 plug both in y+=+a%28x-h%29%5E2+%2B+k and solve for a

6.9=+a%28a-6+%2B6%29%5E2+%2B+2
6.9=+a%2Aa%5E2+%2B+2
6.9-2=+a%5E3
4.9=+a%5E3
root%283%2C4.9%29=+a
a=+2.214
equation will be:
y+=+2.214%28x+%2B6%29%5E2+%2B+2
y+=+2.214%28x%5E2%2B12x+%2B36%29+%2B+2
y+=+2.214x%5E2%2B26.568x+%2B79.704+%2B+2
y+=+2.214x%5E2%2B26.568x+%2B81.704+

check it on a graph: