Question

Given the following function, find:
(a) vertex, (b) axis of symmetry, (c) intercepts, (d) domain, (e) range, (f) intervals where the function is increasing,(g) intervals where the function is decreasing, and (h) the graph of the function f(x)=-x^2-6

Answer 1

find the axis of symmetry x = -b/2a in this question, a = -1, b = 0 and c= -6

so the axis of symmetry is x= 0 or the y-axis

vertex substitute the axis of symmetry value into the original equation

f(0) = -(0)^2 - 2

vertex at (0, -2)

intercepts f(x) = 0 then

-x^2 = 2 or x^2 = -2 no x-axis intercepts as the curve is negative definite

b^-4ac = -8 therefore no real roots

y -intercept x = 0 so (0.-2)

domain: all real x

range: all real y