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

Algebra.Com
Question 1191498: Write a quadratic equation for the parabola that passes through the point (5,-3) and vertex (3,5)
Answer by ikleyn(52803)   (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  =  = -2.


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

Solved.



RELATED QUESTIONS

Suppose a parabola has vertex (5, –3) and also passes through the point (6, 1). Write... (answered by MathLover1)
Find the equation of the quadratic with vertex (-3,-5) that passes through the point... (answered by ewatrrr)
Write the equation of each quadratic relation in vertex form for a parabola that has a... (answered by josgarithmetic)
Write a quadratic function for the parabola that passes through the point (2, -3) with... (answered by josgarithmetic)
Write and graph an equation for the parabola that has vertex (-1, 3) and passes through... (answered by lwsshak3)
Find a function whose graph is a parabola with vertex (4,-6) and that passes through the (answered by ikleyn)
write the equation in both vertex form and standard form for a parabola that has a vertex (answered by josgarithmetic)
Write the standard form of the quadratic function with a vertex of (-3, 5) that passes... (answered by josgarithmetic)
How do I write the equation for this parabola? It's vertex is (5, -3) and passes through (answered by josgarithmetic)