How do I find the vertex, axis of symmetry, y-intercept, x-intercept, domain and range of #f(x) = −4(x − 8)^2 + 3#?

1 Answer
bp
Oct 8, 2015

vertex is (8,3). Axis of symmetry is x=8. x intercepts are #8+-sqrt3/2# . y intercept is (0, -253). Domain #{x:x in RR, -oo<=x <= +oo}#. Range is #{y: y inRR, 3>= y>= -oo}#

Explanation:

The given equation is already given in vertex form. The figure is an vertical parabola, opening down ward. The vertex is (8,3), axis of symmetry is x-8=0 that is x=8. In the given equation put, x=0 to obtain y= -253. Hence y- intercept is (0, -253). For x intercepts put f(x)=0 and solve for x to get x= #8+-sqrt3/2#

domain is whole of real numbers as x can have any real value.
Domain #{x:x in RR, -oo<=x <= +oo}#. Range is #{y: y inRR, 3>= y>= -oo}#

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