Question

What is the vertex for the graph of y = 2x2 + 12x + 10?

Answer 1

2x^2

Answer 2

you can find the vertex for a vertical parabola of that type by using => \(\bf \left(-\cfrac{b}{2a}, c-\cfrac{b^2}{4a}\right)\)

Answer 3

I use the ^ to indicate the exponent. So the equation would be written:

y = 2x^2 + 12x + 10
= 2 (x + 1) (x + 5)
so this parabola intersects the x axis at x=-1 and x=-5.

The midpoint between them is the x-coordinate of the vertex:
[(-1) + (-5)] / 2 = -3
and the y-coordinate is given by the function at that point:
y = 2 * (-3)^2 + 12 (-3) + 10
= 18 - 36 + 10 = -8

The vertex is (-3, -8).

Answer 4

another way to find the vertex is to convert the function to vertex form
2x^2 + 12x + 10
= 2 (x^2 + 6x + 5)
= 2((x + 3)^2 - 9 + 5)
= 2 (x + 3)^2 - 4)
= 2 (x + 3)^2 - 8

the vertex is at the point where (x +3) = 0 i.e. x = -3
and y = -8

vertex is (-3, -8)