The standard form of the parabola is:
Since we have for some constant c.
We know reaches maxima/minima when .
Can you figure out c with this information and write f(x) in standard form?
I am having trouble solving this problem. Any help would be appreciated!
A parabola has x-intercepts at (-2, 0) and (6, 0). Its maximum y-value is 12. Write the standard form of the equation of this parabola.
If its max y-value is 12, the y-value of the vertex is 12, right? I know I should be able to use one of the given x values to find what I need to write the equation, but I just don't know where to start with this...
Hello, Frontier!
Did you make a sketch?A parabola has x-intercepts at (-2, 0) and (6, 0).
Its maximum y-value is 12.
Write the standard form of the equation of this parabola.From the symmetry, we see that the vertex is at (2, 12).Code:| (2,12) | * *| : * * | : * * | : * | : - - * - - + - + - - - - * - - -2 | 2 6
The general equation of a parabola is: .
We know three points on the parabola: .
. . Use these point to create a system of equations.
Subtract: [2] - [1]: .
Subtract: [3] - [2]: .
Substitute [4]: .
Substitute [4] and [5] into [1]: .
Therefore: .
Edit: Dinkydoe has a much better solution!'.