Question

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

1) What are the x-intercepts of the graph representing f?

2) What are the x- and y-coordinates of the vertex of the graph?

please help!!

Answer 1

x-intercepts = -4 and 2

vertex (-1, -9)

Explanation:

To find the x-intercepts ie roots

set the equation to 0

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

From the zero product rule

x - 2 = 0

x = 2

x + 4 = 0

x = -4

x-intercepts = -4 and 2

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The x coordinate of the vertex is the midpoint of the roots

x = (-4 + 2)/2

x = -1

Plug x = -1 into the function

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

y = -3 * 3

y = -9

vertex (-1, -9)