Question

Please help me on this math question

Answer 1

The vertex is at (-1/2, -4 1/2)

Explanation:

y = 2x^2 +2x - 4

y = 2( x^2 +x ) -4

We want to complete the square

b=1 take (b/2)^2 = (1/2)^2 = 1/4 There is a factor of 2 on the outside of the parentheses so we are really adding 2/4 or 1/2, so we need to subtract 1/2

y = 2( x^2 +x +1/4) - 1/2 -4

y = 2 ( x + 1/2)^2 - 4 1/2

This is in vertex form

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

where (h,k) is the vertex

h= -1/2 and k = -4 1/2

The vertex is at (-1/2, -4 1/2)