To find the x-intercepts of the graph, we need to solve for when f(x) = 0.
f(x) = (x - 2)(x + 4) = 0
Setting each factor to zero and solving for x, we get:
x - 2 = 0 or x + 4 = 0 x = 2 or x = -4
Therefore, the x-intercepts of the graph are (2, 0) and (-4, 0).
To find the vertex of the graph, we can use the formula x = -b / (2a) to find the x-coordinate, and then substitute that value into the function to find the corresponding y-coordinate.
f(x) = (x - 2)(x + 4) = x^2 + 2x - 8
a = 1, b = 2
x = -b / (2a) = -2 / (2*1) = -1
f(-1) = (-1)^2 + 2(-1) - 8 = -7
Therefore, the vertex of the graph is (-1, -7).
To find the y-intercept, we can substitute x = 0 into the function and solve for f(x).
f(x) = (x - 2)(x + 4) = x^2 + 2x - 8
f(0) = (0)^2 + 2(0) - 8 = -8
Therefore, the y-intercept of the graph is (0, -8).
Here's a sketch of the graph:
^
|
4 | x
| x
| x
2 | x x
| x x
| x
0--+------------->
|-4 -2 0 2 4
The graph is a parabola that opens upwards and has x-intercepts at (2, 0) and (-4, 0), a y-intercept at (0, -8), and a vertex at (-1, -7).