Quadratic Functions Problem #1 [Precalculus]

Quadratic Functions #1 Question:

Annika is making a fabric memo board. The width of the board is x inches, and the length of the board is (x+4) inches.
a) Write a function that represents the area A of the memo board.
b) Graph the function
c) If the width of the memo board is 8 inches, what is its area?


Answer:

For the quadratic function #1 problem:

Let x be the width of the board.
Let x+4 be the length of the board.

a) Write a function that represents the area A of the memo board.

The area for a rectangular board can be solved by multiplying its width x and its length x+4.

$$A=x(x+4)$$
$$A=x^2 + 4x$$

b) Graph the function.

The graph of the function $$A=x^2+4x$$ would be:

c) If the width of the memo board is 8 inches, what is its area?

Let x = 8.

Plugging 8 as the value of x would result to:

$$A=(8)^2 + 4*8$$
$$A=96in^2$$

If the width of the memo board is 8 inches, the area would be $$96in^2$$.


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