Quadratic function

Question

f(x)= x² -4x

a. the domain
b. the vertex
c. the axis of symmetry
d. the x-intercept(s)
e. the y-intercept
f. the maximum or minimum value of the function
h. State the range.
i. State the interval over which the function is decreasing.
j. State the interval over which the function is increasing.

Answer 1

I will put this function in vertex form.

 

f(x) = (x² - 4x + 4) - 4

 

f(x) = (x - 2)² - 4

 

 

The domain of any polynomial function is all real numbers.

 

From the vertex form of the function, the vertex is (2, -4).  The axis of symmetry is the x-coordinate of the vertex.

 

To find the x-intercepts, set f(x) equal to zero and solve for x.

To find the y-intercept, evaluate f(0).

 

In a quadratic function that has a positive leading coefficient, your vertex is the minimum value.  Therefore, range is in the interval [minimum, ∞).

 

In a quadratic function that has a negative leading coefficient, your vertex is the maximum value.  Therefore, range is in the interval (-∞, maximum].

 

 

You now have all the information need to complete the rest.  Do the same for the other question you have posted.