How do you graph y=x2+3x+2?

1 Answer
May 1, 2016

The obvious method, but the least interesting is to choose x values, work out the corresponding y values and then plot the points. At least 5 or 7 points would be required to ensure some accuracy.

Explanation:

However, a more interesting method is to determine specific important points on the graph using algebra and then plot only those. The points are: the y intercept, the two x intercepts and the turning point (TP), which lies on the axis of symmetry.

For the y-intercept make x = 0.
This will give the constant as the y-intercept. y = 2.

For the x-intercepts make y = 0 and factorise.
The x-intercepts are also known as the roots of the equation.

If y=(x+2)(x+1), then 0=(x+2)(x+1)
So x=2,orx=1

The line of symmetry lies halfway between the xintercepts, giving (2)+(1)2=1.5
This can also be found from the formula x=b2a

The y value of the TP can be calculated by substituting x=1.5 into the original equation, giving y=14.

Plot these 4 points (0,2) ; (-2,0) ; (-1, 0) and (-112,14).
Join them with a smooth hand-drawn line and you have the graph.