How do you use the important points to sketch the graph of y=x^2+5x+3?

1 Answer
Nov 21, 2017

A=(-0.7,0)
B=(-4.3,0)
C=(0,3)
D=(-2.5,-3.25) min

Explanation:

y=0 => x^2+5x+3=0
=>
x_(1,2)=(-5+-sqrt(5^2-4*1*3))/(2*1)=(-5+-sqrt13)/2
=>
x_1=(-5+sqrt13)/2~~-0.7
x_2=(-5-sqrt13)/2~~-4.3
=>
A=(-0.7,0)
B=(-4.3,0)


x=0 => y=0^2+5*0+3=3
=>
C=(0,3)


MAX or MIN:
1) a=1>0 => y "smiles" => MIN
2) y'=2x+5
=>
y'=0 => 2x+5=0 => x=-5/2=-2.5
=>
y_((-2.5))=(-2.5)^2+5*(-2.5)+3=-3.25
=>
D=(-2.5,-3.25) min

graph (in order to check that all match):
graph{x^2+5x+3 [-10, 10, -5, 5]}