Explain the procedure for graphing the quadratic function in factored form f(x) = (x - 2)(x + 4).

Answer 1

First find the x intercepts or zeros by setting the equation equal to zero

(x-2)(x+4)=0 so x= 2 and -4 our zeros . This gives us the points (2,0) and (-4,0)

Next find the vertex. Since parabolas are symmetric the x coordinate of the vertex will lie mid way between 0 and -4 which would be -1

Substitute -1 for x in the original equation to get the y coordinate

y= ( -1-2) (-1+4)

y= (-3)(3)so the coordinates of the vertex are ( -1,-9)

Using these 3 points we can graph the parabola

If you want additional points you can pick any other x value and plug it in the original equation to calculate y for that given x

Answer 2

The first thing to do in order to graph this is to realize that a function in the form f(x)=(x-r1)(x-r2)...(x-rn-1)(x-rn) has n roots, and each of these roots is equal to its r value. The next thing to notice is that the function will have a degree of n, and when zoomed out sufficiently, the graph will look like the graph of the first term, therefore, end behavior is determined by the first term. In the example you gave, the expanded function is f(x)=x^2+2x-8. So, the graph will have the behavior of the graph f(x)=x^2. To plot this, you can see that the graph will have x-intercepts at x=2 and -4, and will have a y-intercept of y=-8. You can also find the vertex of the graph by using the fact that the x-value of the vertex = -b/2a (-2/2 for this function) and a y-value of f(x-value of the vertex) (f(-1) for this function which is -9). So we now have 4 points that we can graph, (-4,0), (-1,-9), (0,-8), and (2,0). After plotting these, simply use the end behavior to finish it off.