SOLUTION: Give the vertex, axis, x-intercepts, y-intercept, domain, and range of the graph of the function: f(x)= (-2/3)((x-6))^2 + 7

Algebra ->  Functions -> SOLUTION: Give the vertex, axis, x-intercepts, y-intercept, domain, and range of the graph of the function: f(x)= (-2/3)((x-6))^2 + 7      Log On


   

Question 1046635: Give the vertex, axis, x-intercepts, y-intercept, domain, and range of the graph of the function:
f(x)= (-2/3)((x-6))^2 + 7
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
It's in vertex for so,
Vertex : (6,7)
Domain : All reals
Range: Since quadratic multiplier is negative, 7 is maximum. (-infinity,7]
Y Intercept, set x=0
y=-%282%2F3%29%280-6%29%5E2%2B7
y=-%282%2F3%29%2836%29%2B7
y=-24%2B7
y=-17
(0,-17)
X intercept, set y=0
0=-%282%2F3%29%28x-6%29%5E2%2B7
%282%2F3%29%28x-6%29%5E2=7
%28x-6%29%5E2=21%2F2
x-6=0+%2B-+sqrt%2821%2F2%29
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x=6+%2B-+sqrt%2821%2F2%29
x=6+%2B-+sqrt%2842%29%2F2