Find the range of f in fx-x2 -4x 5?

Answer 1

F(x) = -x^2 - 4x + 5

This is a quadratic function of the form y = ax + by + c, whose graph is a parabola. So,

a = -1, b = -4 and c = 5

Since a is negative the parabola opens downward, and the maximum valy of the function is equal to the value of the y-coordinate of the vertex.

The x- coordinate of the vertex is x = -b/2a. So,

x = -(-4)/[2(-1) = 4/-2 = -2 When x = -2, then

y = -(-2)^2 - 4(-2) + 5 = -4 + 8 + 5 = 9

Thus, the range is all value of y, such that y ≤ 9, Equivalently, the range is {y| y ≤ 9} or

[9, ∞).