Answer:
[tex]y=\frac{1}{2}(x+6)^2-1[/tex]
Step-by-step explanation:
Equation of the Quadratic Function
The vertex form of the quadratic function has the following equation:
[tex]y=a(x-h)^2+k[/tex]
Where (h, k) is the vertex of the parabola that graphically represents the function, and a is a coefficient different from zero.
The vertex of the required equation is located at (-6,-1)
The parabola passes through (-12,17)
Substituting the coordinates of the vertex, the equation of the function is:
[tex]y=a(x+6)^2-1[/tex]
The value of a will be determined by using the given point:
[tex]17=a(-12+6)^2-1[/tex]
Operating:
[tex]17=a(36)-1[/tex]
[tex]36a=18\Rightarrow a=18/36=1/2[/tex]
Solving:
[tex]a=1/2[/tex]
The equation of the parabola is:
[tex]\boxed{y=\frac{1}{2}(x+6)^2-1}[/tex]
