Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. then, rewrite the equation in standard form. [hint: vertex form: y - k = a(x - h)2]

PART A

The equation of the parabola in vertex form is given by the formula,



where



is the vertex of the parabola.

We substitute these values to obtain,



The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.








Hence the equation of the parabola in vertex form is



PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.



This implies that



We expand to obtain,



This will give us,





This equation is now in the form,


where



This is the standard form