Question

Use complete sentences to explain how you would use graphing technology to find the solutions of 0 = 2x2 − 3x + 0.5. What do the solutions of 0 = 2x2 − 3x + 0.5 represent on the graph of the equation?

Answer 1

Hi sumsumjoe,
On my TI-89, there is a 'Y=' section where I can enter equations of lines. I would start by hitting 'green diamond', then 'F1' for 'Y=', and then I would type the right half of the equation in: 2x^2 - 3x + .5
Then I would hit 'green diamond' and 'F3' for 'graph'.
When the graph pops up, it will look something like this:


Note that the graph crosses the x-axis at two points. I've circled them. Wherever the graph crosses the x-axis, y is equal to 0. So this equation 0 = 2x^2 - 3x +.5 is really describing where the curve 'y=2x^2 - 3x +.5' crosses the x-axis, or where y = 0. These two points are known as the 'x intercepts', because the curve 'intercepts' the x-axis.

Furthermore, you can find the solutions to the equation, which in this case contain many decimal places, by moving your cursor to the location where y=0, or where the curve crosses the x-axis, at the previously mentioned x intercepts. If you want an exact number, on the TI 89 you can use the 'F5/Math->Zero' function, and arrow over to a 'lower bound' and 'upper bound' around each intersection; that is, trace the cursor to one side of the intercept for the lower bound, then hit enter, and trace the cursor to the other side of the intercept for the upper bound, and hit enter again. You will be presented with an x-value; this x-value is a solution to the equation, because it outputs a y-value of '0'. Once you run that function once for each intersection (once for the intersection on the left, and once for the intersection on the right), you will have two x-values, which are solutions of your original equation.

In this case, I found two solutions: x=.19098 for the left intersection and x=1.30902 for the right side intersection. Both values were estimated by my calculator to a given number of digits.