This graph represents a quadratic function. What is the function's equation written in factored form and in vertex form?

vertex form:  f (x) = 2 * (x - 2) ^ 2 - 8

factored form: f (x) = 2 * x * (x - 4)

Step-by-step explanation:

The first thing is to calculate the equation with its vertex form, we can calculate it knowing that it is formulated in the following:

f (x) = a * (x - h) ^ 2 + k

where

a is a coefficient

(h, k) is the vertex

Looking at the graph

The vertex is the point (2, -8), we replace and we are left with:

f (x) = a * (x - 2) ^ 2 - 8

Now, to calculate the value of the coefficient we are going to

mark a point on the graph

, we will select (0,0)

and replacing we have:

0 = a * (0 - 2) ^ 2 - 8

0 = 4 * a - 8

a = 8/4

a = 2

Therefore, we would be left with the equation of the function written in The first thing is to calculate the equation with its vertex form, we can calculate it knowing that it is formulated in the following:

f (x) = a * (x - h) ^ 2 + k

where

a is a coefficient

(h, k) is the vertex

Looking at the graph

The vertex is the point (2, -8), we replace and we are left with:

f (x) = a * (x - 2) ^ 2 - 8

Now, to calculate the value of the coefficient we are going to

mark a point on the graph

, we will select (0,0)

and replacing we have:

0 = a * (0 - 2) ^ 2 - 8

0 = 4 * a - 8

a = 8/4

a = 2

Therefore, we would be left with the equation of the function written in vertex form:

f (x) = 2 * (x - 2) ^ 2 - 8

Now for the factored form, we know it has the following structure:

f (x) = a * (x - x1) * (x - x2)

knowing that a is a coefficient

and that x1 and x2 are the zeros or x-intercepts of the function

Looking at the graph

The zeros or x-intercepts of the function are

x = 0 and x = 4

so

f (x) = a * (x - 0) * (x - 4)

f (x) = a * x * (x - 4)

To calculate the value of the coefficient a, we will take the point (2, -8), we replace:

-8 = a * 2 * (2 - 4)

-8 = 4 * a - 8 * a

4 * a = 8

a = 2

we replace and we have:

f (x) = 2 * x * (x - 4) and this would be the factored form of the equation

Now for the factored form, we know it has the following structure:

f (x) = a * (x - x1) * (x - x2)

knowing that a is a coefficient

and that x1 and x2 are the zeros or x-intercepts of the function

Looking at the graph

The zeros or x-intercepts of the function are

x = 0 and x = 4

so

f (x) = a * (x - 0) * (x - 4)

f (x) = a * x * (x - 4)

To calculate the value of the coefficient a, we will take the point (2, -8), we replace:

-8 = a * 2 * (2 - 4)

-8 = 4 * a - 8 * a

4 * a = 8

a = 2

we replace and we have:

f (x) = 2 * x * (x - 4) and this would be the factored form of the equation

"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: