Question

Write the equation for a parabola whose vertex is (-6,-1) and passes through (-12,17).

Answer 1

Answer:

$y=\frac{1}{2}(x+6)^2-1$

Step-by-step explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

$y=a(x-h)^2+k$

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:

$y=a(x+6)^2-1$

The value of a will be determined by using the given point:

$17=a(-12+6)^2-1$

Operating:

$17=a(36)-1$

$36a=18\Rightarrow a=18/36=1/2$

Solving:

$a=1/2$

The equation of the parabola is:

$\boxed{y=\frac{1}{2}(x+6)^2-1}$