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

Nov 1, 2015

Domain is $\mathbb{R}$, range is: [-5 1/12;+oo)

#### Explanation:

As $h \left(x\right)$ is a polynomial, it is defined for all real numbers (its domain is $\mathbb{R}$)

If you look at the graph:
graph{3x^2+5x-3 [-14.24, 14.24, -7.12, 7.13]}

you will see that the range is [q;+oo).

To calculate the coordinates of the vertex $V = \left(p , q\right)$ you can use the following formulas:

$p = - \frac{b}{2 a}$ $q = - \frac{\Delta}{4 a}$

To calculate $q$ you can also substitute the calculated $p$ for $x$ in the formukla of the function