Question

5.In the following equation, identify the x-intercepts in the graph y = 3x2 + 19x – 40. (2 points)

Answer 1

On a graph, the x-intercept is, by definition, where the line intercepts the x axis. The x axis is defined as being the line in a coordinate system where y=0. So to find the x intercepts, plug in 0 for y and solve for x:\[0 = 3x^{2}+19x-40\]Factor the quadratic\[0 = (x+8)(3x-5)\]So looking at this equation now, there are only two ways it can be true: either the first parentheses group is 0 or the 2nd parentheses group is 0. So solve each for 0:\[0 = x+8\]\[x=-8\]And the 2nd one:\[0 = 3x-5\]\[3x = 5\]\[x=\frac{5}{3}\]So the two possible values for x that will make y=0 are x=-8 and x=5/3, and these are also where the graph intercepts the x axis.

Answer 2

thanks