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

Nov 10, 2017

Domain: $x \in \mathbb{R} \mathmr{and} \left(- \infty , \infty\right)$
Range: $y \le 5 \mathmr{and} \left[- \infty , 5\right]$

#### Explanation:

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

having vertex at $\left(10 , 5\right)$ [ 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: $x \in \mathbb{R} \mathmr{and} \left(- \infty , \infty\right)$

Range: Any real number of $y \le 5 \mathmr{and} \left[- \infty , 5\right]$

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