Question

Find the vertex F(x)=-2x^2+2x+6
the x and y intercepts
line of symmetry
max/min value

Answer 1

x = -b/2a = -2/-4=1/2
y = -2(1/2)^2 +2(1/2) + 6 = -2(1/4)+1 + 6= -1/2 + 7 = 6 1/2 so Vertex is (1/2,6 1/2)
Line of symmetry is a vertical line through the vertex so it is x = 1/2
The vertex represents the maximum/minimum. This parabola has a maximum since it is concave downward. The the maximum is 6 1/2
Find the y intercept by letting x = 0 so y = 6 and (0,6) is the y intercept.
Find the x intercepts by letting y = 0 so -2x^2 + 2x + 6 = 0 or -2(x^2 - x - 3) = 0.
Solve that using the quadratic equation.

Answer 2

x = [1 + - sqrt(1-4(1)(-3)]/2 = [1 +- sqrt13]/2