we have that
y = -2x² + 2x +2
Group terms and move the constant to the opposite side of the equation
y -2 = -2x² + 2x
Factor the leading coefficient
y -2 = -2(x²-x )
Complete the square. Remember to balance the equation by adding the same constants to each side
y -2 -0.25*2= -2(x²-x+0.25 )
y -2.50= -2(x²-x+0.25 )
Rewrite as perfect squares
y -2.50= -2(x-0.50)²
Part a) The equation of a parabola in vertex form is. y=a(x−h)2+k
so
y -2.50= -2(x-0.50)²--------> y = -2(x-0.50)²+2.50
the answer Part a) is
y = -2(x-0.50)²+2.50
part b) Find the vertex
we know that the vertex is the point (h,k)
so
(h,k) is the point---------> (0.50,2.50)
the answer part b) is
the vertex is the point (0.50,2.50)
Part c) find the value for x = 6
y = -2(x-0.50)²+2.50-----> y = -2(6-0.50)²+2.50----> y = -2(5.50)²+2.50
y=-60.50+2.50-------> y=-58
the answer Part c) is
-58
