A parabola has a vertex at (-2,6) and roots at 7 and m. Find the value of m

So m = - 11

Step-by-step explanation:

* THe vertex is (-2,6), then the equation is y = a (x+2) ^2 + 6, a is to find out.

* A root is 7 means x=7 and y=0, then:

0 = a (7+2) ^2 + 6

0=81a+6 or a = - 6/81 = - 2/27.

* We have the equation: y = - 2/27 (x+2) ^2 + 6=-2/27 [ (x+2) ^2-81]

y = - 2/27 (x-7) (x+11).

So m = - 11

Hope that you understand.