How to graph y<x^2 + 4x?

Reblausvtct

Reblausvtct

Answered question

2023-02-19

How to graph y < x 2 + 4 x ?

Answer & Explanation

Kylie Woodward

Kylie Woodward

Beginner2023-02-20Added 6 answers

First consider the equation y = x 2 + 4 x . This can be factored as y = x ( x + 4 ) .
Note that this has zeros when y = 0 , which are when x = 0 and x + 4 = 0 x = - 4 .
The vertex of this parabola will be halfway between the zeros, at x = - 2 . Note that y ( - 2 ) = ( - 2 ) 2 + 4 ( - 2 ) = - 4 .
Consequently, it is simple to create a parabola using points ( - 4 , 0 ) , ( - 2 , - 4 ) , ( 0 , 0 ) :
graph{x^2+4x [-14.09, 8.41, -5.855, 5.395]}
We want to find when y < x 2 + 4 x , which will be all points lying below the parabola. Since y < the parabola and not y the parabola, the line of the graph will be dotted:
graph{y < x^2+4x [-14.09, 8.41, -5.855, 5.395]}

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