Question

Find the range of the function f(x)= x²+4x+5.

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Answer 1

f(x) = x²-4x-5, quadratic function,

Domain (the values if x) is all real numbers.

To find range we should draw a graph or to write an equation in vertex form.

f(x) = x²-4x+4-4-5

f(x) = (x-2)²-9

Point (-2,-9) is the vertex of the parabola, and it is a minimum because a parabola has positive sign in front of x², so it is looking up. Minimum value of y =-9

Range(the values of y) is [-9, ∞)