Question

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

(−3, −8)

(−3, −44)

(3, 64)

(3, 58)

Answer 1

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 2

For an equation y = ax^2 + bx + c,

find the x-coordinate of the vertex using\[\large x= \frac{ -b }{2a }\]
Then plug that number back into y = 2x^2 + 12x + 10 to find the y-coordinate of the vertex.