The vertex is (-3,3) and goes through point (-2,6). The equation in vertex form is [tex]y=3(x+3)^{2}+3[/tex]
Solution:
Given that, vertex of a parabola is (-3, 3) and the parabola passes through the point (-2, 6).
We have to find the equation of parabola in vertex form.
The general form of parabola equation in vertex form is given as:
[tex]y=a(x-h)^{2}+k[/tex]
Where (h, k ) is vertex and a is a constant .
Here in our problem, h = -3 and k = 3
Then, parabola equation is given as:
[tex]y=a(x-(-3))^{2}+3 \rightarrow y=a(x+3)^{2}+3[/tex]
Now, we know that it passes through (-2, 6). So substitute x = -2 and y = 6
[tex]\rightarrow 6=a(-2+3)^{2}+3 \rightarrow a(1)^{2}=6-3 \rightarrow a=3[/tex]
So, now parabola equation in vertex form is [tex]y=3(x+3)^{2}+3[/tex]
