SOLUTION: Determine the quadratic function with the given information. Given: vertex (3,-7) and y-intercept of -4 Answer in the form y=a(x-h)^2+k

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine the quadratic function with the given information. Given: vertex (3,-7) and y-intercept of -4 Answer in the form y=a(x-h)^2+k      Log On


   

Question 929218: Determine the quadratic function with the given information.
Given: vertex (3,-7) and y-intercept of -4
Answer in the form y=a(x-h)^2+k
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%28x-3%29%5E2-7


A few simple steps gives
%28y%2B7%29%2F%28x-3%29%5E2=a
which allows you to use the given (0,-4) to evaluate a.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Determine the quadratic function with the given information.
Given: vertex (3,-7) and y-intercept of -4
Answer in the form y=a(x-h)^2+k


y+=+a%28x+-+h%29%5E2+%2B+k ------ Vertex form of parabolic equation

A y-intercept of - 4 signifies coordinate point, (0, - 4)

-+4+=+a%280+-+3%29%5E2+-+7 ------ Substituting all given values in vertex form of paraoblic equation to determine the value of "a"

-+4+=+9a+-+7

9a = - 4 + 7

9a = 3

a = 3%2F9, or 1%2F3

highlight_green%28y+=+%281%2F3%29%28x+-+3%29%5E2+-+7%29 -------- Vertex form of parabolic equation, based on given info