SOLUTION: Write a quadratic function whose graph has the given characteristics: x-intercepts (-1,0),(7,0) and a point on the graph: (3,2). I tried making an equation using both intercepts.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Write a quadratic function whose graph has the given characteristics: x-intercepts (-1,0),(7,0) and a point on the graph: (3,2). I tried making an equation using both intercepts.       Log On


   

Question 560610: Write a quadratic function whose graph has the given characteristics: x-intercepts (-1,0),(7,0) and a point on the graph: (3,2).
I tried making an equation using both intercepts.
x=-1 x=7
x+1=0 x-7=0
(x+1)(x-7)=0
x^2-6x-7=0
So far I have this equation, but I don't know how to make it go through the point (3,2). If anyone could please help me, I would greatly appreciate it.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you know that the x-intercepts are the roots of the function

the axis of symmetry lies midway between the roots ___ x = (-1 + 7) / 2 ___ x = 3

the given point is on the axis of symmetry, so it is the vertex

using the vertex form ___ y = a(x - 3)^2 + 2

plug in one of the intercepts to find the value of a ___ 0 = a(7 - 3)^2 + 2