Find the vertex and graph?

Question

y=-2x^2+2x+2

Answer 1

y = 2x^2 + 2x + 2

To find the vertex, you must complete the square.

First, factor out 2 from the first two terms.

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

Now, add the required number to create a perfect square trinomial. Offset this by subtracting the added value.

y = 2(x^2 + x + 1/4) + 2 - 2(1/4)
y = 2(x + 1/2)^2 + 2 - 1/2
y = 2(x + 1/2)^2 + 4/2 - 1/2
y = 2(x + 1/2)^2 + 3/2

Answer 2

I can't graph the equation here but I can find the vertex.

To find the vertex complete the square.

y = -2x² + 2x + 2

y + -2*(1/4) = -2(x² - x + 1/4) + 2

y - 1/2 = -2(x - 1/2)² + 2

y - 5/2 = -2(x - 1/2)²

The vertex (h,k) = (1/2, 5/2)

Answer 3

Why all that calculation ?

Suppose the equation is
y= A *(x^2) + Bx + C

Vertex can be found easily by taking derivative of the expression and equating it to zero

that is

2Ax + B =0, which means
**************************
*********x= -B/2A*******
**************************

Don't worry. This was just the derivation. The formula is that you find (-B/2A) this is the x co-ordinate of the vertex.

Put this value in expression to find Y co--ordinate.

This is it.
Here,
A = -2
B = 2
C = 2

so x = -2/[2*(-2)] = 1/2.
Fnd y yourself

Answer 4

vertex;
y=-2x^2+2x+2
y=-2(x^2-x+1/4)+5/2
y=-2(x-1/2)^2+5/2
Vertex is (1/2,5/2)