Question

what is the vertex? y=2x^2+28x-8

Answer 1

fist convert the equation to vertex form

y = 2(x^2 + 14x) - 8
 y = 2 [(x + 7)^2 - 49] - 8
y = 2(x + 7)^2 - 106

So the vertex is at (-7,-106)

Answer 2

Put in math terms, the equation we are given is y = 2x² + 28x - 8

This equation is set up in standard form.  Standard form is ax² + bx + c.  In order to find the vertex, we'll complete the following equation:
-b / 2a
-28 / 2 (2)
-28 / 4
-7

Next, we'll just put -7 into the equation in place of x.

2(-7)² + 28(-7) - 8
2(49) -196 - 8
98 - 204
-106

So the vertex is (-7, -106).  Have fun plotting that.

Hope this helps!