SOLUTION: Find an equation in standard form of the parabola described. Vertex at (−4, −2); passes through (−3, 0) and (9/4, 3) standard form: (y-k)^2 =4p(x-h)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find an equation in standard form of the parabola described. Vertex at (−4, −2); passes through (−3, 0) and (9/4, 3) standard form: (y-k)^2 =4p(x-h)      Log On


   

Question 1162555: Find an equation in standard form of the parabola described.
Vertex at (−4, −2); passes through (−3, 0) and (9/4, 3)

standard form: (y-k)^2 =4p(x-h)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given: Vertex at (-4, -2); passes through (-3, 0) and (9%2F4, 3)


standard form:

%28y-k%29%5E2+=4p%28x-h%29 where h and k are coordinates of vertex
since given vertex at (-4, -2), we have
%28y-%28-2%29%29%5E2+=4p%28x-%28-4%29%29
%28y%2B2%29%5E2+=4p%28x%2B4%29 .........eq.1

since passes through (-3,+0), we have
%280-%28-2%29%29%5E2+=4p%28-3-%28-4%29%29
%280%2B2%29%5E2+=4p%28-3%2B4%29
4+=4p%281%29
p=4%2F4
p=1
so, your equation is:
%28y%2B2%29%5E2+=4%28x%2B4%29

and since passes through (9%2F4, 3), check if true:
%283%2B2%29%5E2+=4%289%2F4%2B4%29
5%5E2+=4%289%2F4%29%2B16
25+=9%2B16
25+=25-> true