HEL Use the function f(x) = -16x² + 60x + 16 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph

Here we have the quadratic function:

f(x) = -16*x^2 + 60*x + 16

We can see that it is in standard form:

y = a*x^2 + b*x + c

a) First we want to completely factorize the function f(x).

To do it, we first need to find the roots of f(x).

Remember that for a generic quadratic equation:

a*x^2 + b*x + c = 0

whit roots x₁ and x₂, the factorized form is:

a*(x - x₁)*(x - x₂)

And the roots are given by:

Then for the case of f(x) = -16*x^2 + 60*x + 16, the roots are:

So the two roots are:

x₁ = (-60 + 68)/-32 = -0.25

x₂ = (-60 - 68)/-32 = 4

Then the factorized form is:

f(x) = -16*(x - 4)*(x + 0.25)

B) We already found the roots, which are:

x₁ =  -0.25

x₂ =  4

These are the x-intercepts:

(-0.25, 0) and (4, 0)

C) We can see that the leading coefficient is negative.

This means that the arms of the graph go downwards, so as |x| increases, the value of f(x) tends to negative infinity.

D) To graph f(x) we can find some of the points of the graph (like the x-intercepts and some more of them) and then connect them with a parabola curve, the graph that you will get is the one that you can see below.

If you want to learn more about this topic, you can read:

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

1010: 3030

is it i think