1) The x-intercepts of the graph representing f are; 2 and 4
2) The x- and y-coordinates of the vertex of the graph are; (1, -5)
3) The y-intercept is at; (0, -8)
We are given the function; f(x) = (x - 2)(x + 4)
1) The x-intercepts of a graph are the points where the graph crosses the x-axis. The x-intercepts are the value of x when f(x) = 0. Thus, the x-intercepts here are 2 and 4.
2) The vertex is the lowest point of the graph in this case as the parabola opens upwards.
Let us expand the function to get;
f(x) = x² - 2x + 4x - 8
f(x) = x² + 2x - 8
where; a = 1, b = 2, c = -8
Formula for the x-coordinate of the vertex is;
x = -b/2a
x = -2/2(1)
x = 1
Thus;
y = (1 - 2)(1 + 4)
y = -5
x- and y-coordinates of the vertex of the graph are; (1, -5)
3) The y-intercept is the point at which x = 0. Thus;
y = 0² + 2(0) - 8
y = -8
The y-intercept is (0, -8).
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