The graph of the parabola and straight line are as follows:

1234-1-2-3-410-10-20xyOpen image in a new page

Graphs of `y = 3x-4` and `y=6-2x^2`.

We can see from the graph that there are 2 solutions, since there are 2 places where the graphs intersect. They are:

(a) At left, approximately (−3.2, −13).

Using computer graphing software (like Scientific Notebook), we can zoom in and find the solution correct to as many decimal places as we like. A few zooms gives us (-3.1085, -13.3255).

-3.108-3.1082-3.1084-3.1086-3.1088-3.109-13.325-13.3255-13.326Open image in a new page

Graphs of `y = 3x-4` and `y=6-2x^2`.

(b) At right, approximately (1.5, 1). Using a computer (or graphics calculator), we can zoom in on this intersection to get a better estimate of (1.6085, 0.8255).

1.6081.60821.60841.60861.60881.6090.82450.8250.82550.8260.82650.827xOpen image in a new page

Graphs of `y = 3x-4` and `y=6-2x^2`.

Get the Daily Math Tweet!
IntMath on Twitter