consider the quadratic function

Question

Consider the quadratic function f(x)=-2x²+2x+4

a) Express f(x) in standard form

b) Find its vertex and indicate if it is the maximum or the minimum of f

Answer 1

a) Standard form
-2x2 + 2x + 4 = 0

b) x coordinate of vertex can be found by using x = -b/(2a)


x = -(2)/(2)(-2) = -2/-4 = 1/2

f(1/2) will give you the y coordinate of the vertex.

f(1/2) = -2(1/2)² + 2(1/2) + 4

= -2(1/4) + 1 + 4

= -1/2 + 5 = 4 1/2 or 9/2

Vertex is (1/2, 9/2)

Since the coefficient of the x² term is negative, the parabola is open downward and therefore the vertex is a maximum.