Question

How do you graph `Y=x^2+5x+3`?

Answer 1

We can use a trick to create an identity which will make it easier for us to identify the function and graph it properly..

`y=x^2+5x+3=x^2+2 5/2x+25/4-13/4=(x^2+2 5/2x+25/4)-13/4`

`=(x+5/2)^2-13/4`

• `(x+5/2)^2` is the parabola graph with vertex: minimum at `(-5/2,0)`,

• `(x+5/2)^2-13/4` is the graph of `(x+5/2)^2` shifted `13/4` points downwards.