Answer :
The vertex form of a parabola equation is the following:
[tex]y=a(x-h)^2+k[/tex]Where (h, k) is the vertex of the parabola. The vertex is (h, k) = (-3, 5). Replacing in the formula:
[tex]y=a(x+3)^2+5[/tex]To determine the value of "a" we replace the point (x, y) = (0, 14). Replacing we get:
[tex]14=a(0+3)^2+5[/tex]We solve for "a" first by subtracting 5 to both sides:
[tex]14-5=a(3)^2[/tex]Solving the operations:
[tex]9=9a[/tex]Dividing both sides by 9 we get:
[tex]\begin{gathered} \frac{9}{9}=a \\ 1=a \end{gathered}[/tex]Replacing the value of "a":
[tex]y=(x+3)^2+5[/tex]The standard form of the parabola equation is:
[tex]y=ax^2+bx+c[/tex]we can take the given equation by solving the square:
[tex]y=x^2+6x+9+5[/tex]Solving the operations:
[tex]y=x^2+6x+14[/tex]