Question

The function f is given by f(x)= (x-2) (x+4) . Without using graphing technology, answer the following questions.

Answer 1

Answer:

Step-by-step explanation:

1. What are the x-intercepts of the graph representing f?  They are the points on the horizontal axis where the graph touches or crosses the axis.  Note that on this axis, y = 0.

2. What are the x- and y-coordinates of the vertex of the graph?  Since the function is written as the product of two binomials, we can take these coordinates directly from the binomials:  (x - 2) yields x = 2 and (x + 4) yields x = -4.

3. What is the y-intercept?   Multiply out these binomials.  We get:

f(x) = x^2 + 2 - 8.   When x = 0, y = -8.  The y-intercept is (0, -8).