What is the domain and range of $y=-3(x-10)^2+5$ ?

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Answer 1 · 2017-11-10T12:05:23

Domain: $x in RR or (-oo,oo)$
Range: $y<=5 or [-oo,5]$

$y= -3(x-10)^2+5$ . This is vertex form of equation of parabola

having vertex at $(10,5)$ [ Comparing with vertex form of

equation $f(x) = a(x-h)^2+k ; (h,k)$ being vertex we find

here $h=10 , k=5 , a=-3$ ] . Since $a$ is negative the parabola

opens downward , vertex is the maximum point of $y$ .

Domain: Any real number of $x$ is possible as input.

So Domain: $x in RR or (-oo,oo)$

Range: Any real number of $y<=5 or [-oo,5]$

graph{-3(x-10)^2+5 [-20, 20, -10, 10]} [Ans]

What is the domain and range of y=-3(x-10)^2+5 y=-3(x-10)^2+5?