1. consider the function f(x) = (x + 4)(x – 2). (a) what are the x-intercepts of the graph of the function? (b) what is the equation of the axis of symmetry? explain how you know. (c) what is the vertex of the function? show your work. (d) graph the function. there should be a graph here but i dont know how to upload it

The x intercepts are where the graph crosses or touches the x axis.

To find these answers, set f(x) equal to zero and solve for x

f(x) = 0

(x+4)(x-2) = 0

x+4=0 or x-2 = 0 ... zero product property

x = -4 or x = 2

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The axis of symmetry cuts the parabola into two equal mirrored or symmetric halves (one side folds over the axis of symmetry to land on the other). Because of this nice symmetry, the roots are spaced in such a way that the midpoint of the segment AB is going to be where the axis of symmetry touches the x axis. In this case A and B are the two roots. So add up A and B, then divide by 2 to get: (A+B)/2 = (-4+2)/2 = (-2)/2 = -1

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This is the lowest point of the parabola (aka global minimum)

Use the answer from part (b) to find the y coordinate of the vertex. The axis of symmetry always passes through the x coordinate of the vertex.

f(x) = (x+4)(x-2)

f(-1) = (-1+4)(-1-2) ... replace x with -1

f(-1) = (3)(-3)

f(-1) = -9

When x = -1 is plugged in, it leads to the output y = -9. So x = -1 and y = -9 pair up to form the ordered pair (x,y) = (-1,-9)

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I suggest using a graphing calculator. If you don't have one, then use a free online tool such as GeoGebra or Desmos. I prefer GeoGebra, which is what I used to make the graph shown below. To do this by hand, you plug in various x values to get corresponding y values. This produces various points to plot. Graphing the points and drawing a curve through them will produce the parabola shown in the image.

muyb ajo

step-by-step explanation:

jegosu

step-by-step explanation: