SOLUTION: Write a quadratic equation for the parabola that passes through the point (5,-3) and vertex (3,5)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a quadratic equation for the parabola that passes through the point (5,-3) and vertex (3,5)      Log On


   

Question 1191498: Write a quadratic equation for the parabola that passes through the point (5,-3) and vertex (3,5)
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.
Write a quadratic equation for the parabola that passes through the point (5,-3) and vertex (3,5)
~~~~~~~~~~~~~~~~~ 

Vertex form of the parabola is

    y = a*(x-3)^2 + 5.


To find the unknown coefficient "a", use the fact that the given point (5,-3) belongs to the parabola

    -3 = a*(5-3)^2 + 5.


It gives

    -3 - 5 = a*2^2

       -8  = 4a

        a  = -8%2F%284%29 = -2.


Thus the parabola is  y = -2(x-3)^2 + 5.    ANSWER

Solved.