SOLUTION: Y = ax^2 + 4x + c the maximum is at (1,8) the left hand side starts at (-1,0) it goes through (0,6) and reaches the maximum then goes down an end at (3,0) i need to know t

Question 203258: Y = ax^2 + 4x + c
the maximum is at (1,8)
the left hand side starts at (-1,0)
it goes through (0,6) and reaches the maximum then goes down an end at (3,0)
i need to know the value of c and a.
I have been stuck on this question for a long time. thank you again
i dont even know how to get started.
thank you for taking your time to solve this.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Given:

Find a and c.
First, you are told that the maximum (vertex) of the parabola is at (1, 8).
The value of the x-coordinate of the vertex is given by:
Substitute b = 4 and x = 1 (from (1, 8)) to get:
Multiply both sides by a.
Simplify.
so we have...
Now to find the value of c, just substitute the x- and y-coordinates of any of the points given in the problem. (1, 8) or (-1, 0) or (0, 6) or (3, 0).
The reason you can do this is because every one of these points lies on the curve (parabola) and thus satisfies the given equation.
Let's choose the point (0, 6).
Simplify.

The equation is:

Let's see what the curve looks like!

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