## meg_poo Group Title Suppose a parabola has an axis of symmetry at x = –7, a maximum height of 4, and also passes through the point (–6, 0). Write the equation of the parabola in vertex form. one year ago one year ago

1. tcarroll010

Since you have an axis of symmetry at x = -7 and a maximum height of 4, you have the additional point of (-7,4) for the parabola. From symmetry, you have point (-8,0). If you use y = ax^2 + bx + c, you can set up 3 linear equations in 3 unknowns and solve for a, b, and c.

2. meg_poo

so like this would be the vertex equation y=-4x^2-56x-192

3. tcarroll010

You have the point (-6,0) from your problem statement plus the 2 points I gave you for 3 points total. Now that you have 3 points, and since they are not collinear (all on the same line), they uniquely determine a polynomial of degree 2, which is a parabola. If you use the equation I gave you and set up 3 substitutions, you will have 3 equations in the unknowns of a, b, and c. So you just have to solve a linear system. Once you get to that point with these 3 points, it's a piece of cake.

4. tcarroll010

Yes, that would be the form, but first you have to solve for a, b, and c from the method I outlined.

5. tcarroll010

Yes, you've got it now.