Answer:
(5/2, 29/2), and this represents a maximum
Step-by-step explanation:
g(x) = -2x^2 + 10x + 2 is a quadratic function with coefficients {-2, 10, 2}.
The formula for the axis of symmetry (which passes through the vertex) is
x = -b/ [2a]. Here, a = -2; b = 10. Therefore, the axis of symmetry is
x = -10/ [2(-2)] = -10/(-4) = 5/2
Evaluate the function g(x) = -2x^2 + 10x + 2 at x = 5/2 to determine the y-coordinate of the vertex:
g(5/2) = -2(5/2)^2 + 10(5/2) + 2, or
g(5/2) = -2(25/4) + 25 + 2, or
g(5/2) = -25/2 + 27, or
g(5/2) = 14.5
The vertex is thus (5/2, 29/2), and this represents a maximum, because the coefficient of the x^2 term is negative (the curve opens downward).
