Question

7. Write the quadratic below in its vertex form and then state the coordinates of its turning point. Show how you arrived at your answers. Complete the square! y=x² +18x-12

Answer 1

the equation:

`y=x^2+18x-12`

has the form:

`y=ax^2+bx+c^{}`

where a = 1, b = 18, and c= -12.

To complete the square, we need to add and subtract, the next term:

`((b)/(2))^2`

In this case:

`((18)/(2))^2=9^2=81`

Adding and subtracting 81 to the parabola, we get:

`\begin{gathered} y=x^2+18x-12+81-81 \\ y=(x^2+18x+81)+(-12-81) \\ y=(x+9)^2-93 \end{gathered}`

This equation has the form (the vertex form):

`y=(x-h)^2+k`

where (h,k) is the vertex of the parabola. Then, the turning point (vertex) is (-9, -93)