Write function about area of rectangle. Height is x+2 and length is 20-2x. Show that fubction fits the definition of a quadratix function. Thenx ;)
area = (x+2)(20-2x)
= 20x - 2x^2 + 40 -4x
= -2x^2 + 16x + 40
which is a quadratic function because of the -2x^2 term
What would be the domain and range of this equation oh great lord reiny
Or anyone else
as with all polynomials, the domain is (-∞,∞)
area = 72-2(x-4)^2
You can see that its maximum value is at x=4, since then (x-4)=0 and nothing is subtracted from 72.
So, the range is (-∞,72]
To find the area of a rectangle, you multiply the length and the height. In this case, the length is given as 20 - 2x, and the height is x + 2. We can write the function for the area of the rectangle as follows:
A(x) = (20 - 2x)*(x + 2)
Now, let's verify whether this function fits the definition of a quadratic function. In general, a quadratic function is a function of the form:
f(x) = ax^2 + bx + c
In our case, the function A(x) = (20 - 2x)*(x + 2) is not in the standard quadratic form. We can expand and simplify it to check if it can be written in the quadratic form:
A(x) = (20 - 2x)*(x + 2)
= 20x + 40 - 2x^2 - 4x
Now, let's see if we can rewrite it in the form ax^2 + bx + c:
A(x) = -2x^2 + 20x - 4x + 40
= -2x^2 + 16x + 40
As you can see, the function A(x) can be written in the standard quadratic form, where a = -2, b = 16, and c = 40. Therefore, the function A(x) fits the definition of a quadratic function.
I hope this explanation helps! If you have any further questions, feel free to ask.