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

1 Answer
May 1, 2016

The obvious method, but the least interesting is to choose xx values, work out the corresponding yy 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 -y intercept, the two x -x intercepts and the turning point (TP), which lies on the axis of symmetry.

For the yy-intercept make xx = 0.
This will give the constant as the yy-intercept. yy = 2.

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

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

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

The yy value of the TP can be calculated by substituting x= 1.5x=1.5 into the original equation, giving y = -1/4y=14.

Plot these 4 points (0,2) ; (-2,0) ; (-1, 0) and (-11/2, -1/412,14).
Join them with a smooth hand-drawn line and you have the graph.