What's the standard form, vertex, and factored

1)

2)

3)

Step-by-step explanation:

So we have a graph and we know that its roots are at x=-1 and x=3.

We also know the vertex is at (1,-4). With that, we can figure out the three forms.

Factored Form:

The factored form, as given, is:

We already know the roots of -1 and 3. So, substitute:

Simplify:

Now, we just need to figure out a. To do so, we can use the vertex. Since the vertex is at (1,-4), this means that f(1) is -4. So, substitute 1 for x and substitute -4 for f(x):

Add and subtract:

Multiply:

Divide both sides by -4:

So, our factored form is:

Vertex Form:

The vertex form is:

Where (h,k) is the vertex.

We already know the vertex is (1,-4), so substitute 1 for h and -4 for k.

We also previously determined that a is 1, so substitute that also. So:

Simplify:

Standard Form:

To acquire the standard form, simply expand the factored or vertex form. I'm going to expand the factored form:

FOIL:

Combine like terms:

And we're done!

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

let's start from the lower value, we have:

(we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

so, the range of wavelength of infrared radiation is: