Finding the vertex

Question

How do you find the vertex of y = 2x² + 11x + 5?

Answer 1

Use Completion of the Square to convert to vertex form.

Answer 2

To find the x coordinate of the vertex, use the formula x = -b/(2a) Plugging in your values (-11)/((2)(2)) = -11/4

Now, plug this x value into the equation to find the y value.

y=2(-11/4)²+11(-11/4)+5= -81/8

The vertex is at (-11/4, -81/8)

Answer 3

y = 2x^2 + 11x + 5

put it in the general standard vertex form y = a(x-h)^2 + k, where (h,k) is the vertex

y = 2(x^2 + 11x/2 ) + 5

y = 2(x^2 + 11x/2 + (11/4)^2) + 5 - 2(11/4)^2

y = 2(x + 11/4)^2 + 5 - 121/8

y = 2(x + 11/4)^2 + (40-121)/8

y = 2(x+ 2.75)^2 - 81/8

y= 2(x+ 2.75)^2 - 10 1/8

y = 2(x+2.75)^2 - 10.125

vertex is (-2.75, -10.125)