Consider the function fxx224 Find the coordinates of the ver

Consider the function: f(x)=(x-2)²-4

Find the coordinates of the vertex, (x,y)

Find the x-intercepts. State your final answers using the ordered pair notation, (x,0)

Find the y-intercept. State your final answer using the ordered pair notation,(0,y)

Determine if the vertex is a maximum point or minimum point. Explain your answer

Determine where the function f(x) is increasing and decreasing. State your final answers using interval notation.

Sketch a graph of the function f(x), indicating appropriate x&y scales. Be sure to label the given function, the vertex, and intercepts. Choose your x&y scales wisely as the graph must fit on the provided grid. Accuracy counts!

Solution

f(x)=(x-2)^2-4 = x^2 - 4x = 0

a = 1, b = -4

a) x - coordinates of the vertex = -b/2a = 4/2 = 2

y - coordinates of the vertex = f(2) = 4 - 8 = -4

Then vertex = (2, -4)

For the x-intercepts =====> y = 0 = x^2 - 4x =====> x = 0, 4 ======> (4, 0) and (0, 0)

For the y-intercepts =====> x = 0 then y = 0 =====> (0, 0)

Here the vertex is a minimum point =======> a = 1 > 0

Here f\'(x) = 2x - 4 . It will be  increasing and decreasing if  f\'(x) > 0 or  f\'(x) < 0