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

1 Answer
Nov 1, 2015

Answer:

Domain is #RR#, range is: #[-5 1/12;+oo)#

Explanation:

As #h(x)# is a polynomial, it is defined for all real numbers (its domain is #RR#)

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=(p,q)# you can use the following formulas:

#p=-b/(2a)# #q=-Delta/(4a)#

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