The equation for a parabola can also be written in the "vertex form":
[tex]y = a (x-h) ^ 2 + k
[/tex]
Where,
the vertex of the parabola is the point (h, k).
The value of a is the term that accompanies x ^ 2
Substituting values we have:
[tex]y = a (x - (- 4)) ^ 2 + 7
[/tex]
Rewriting we have:
[tex]y = a (x + 4) ^ 2 + 7
[/tex]
For the point (-3, 8) we have:
[tex]8 = a (-3 + 4) ^ 2 + 7
[/tex]
From here, we clear the value of a:
[tex]8 = a (1) ^ 2 + 7
8 = a + 7
a = 8 - 7
a = 1[/tex]
Then, the equation is given by:
[tex]y = (x + 4) ^ 2 + 7[/tex]
Answer:
The equation of the parabola in vertex form is:
[tex]y = (x + 4) ^ 2 + 7[/tex]
