Which statements are true about the graph of the function f(x) = x2 – 8x + 5? check all that apply.

the function in vertex form is f(x) = (x – 4)2 – 11.
the vertex of the function is (–8, 5).
the axis of symmetry is x = 5.
the y-intercept of the function is (0, 5).
the function crosses the x-axis twice.

The correct options are,

The function in vertex form is .

The y-intercept of the function is (0, 5).

The function crosses the x-axis twice.

Step-by-step explanation:

Here the given equation is,

Which is an equation of upward parabola ( leading coefficient is positive ), along y-axis,

We know that,

For the quadratic equation ,

The axis of symmetry is,

By comparing,

The axis of symmetry of the given function would be,

Now, add and subtract 16 on the right side in equation (1),

Which is the required vertex form of the given equation,

In the vertex form , (h,k) is called vertex,

By comparing,

The vertex of the equation (1) is (4,-11),

For y intercept, substitute x = 0 in equation (1),

Thus, the y-intercept of the given function is (0,5).

Since, when f(x) =0,

Hence, the x-intercepts of the given function are, (4+√11,0) and (4-√11,0),

⇒ The function crosses the x-axis twice.

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation:

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.