Question

A rectangular picture measuring 5 in. by 9 in. is surrounded by a frame with uniform width x.Write a quadratic function in standard form to show the combined area of the picture and frame.f(x) - 8x+ 28f(x) - 4x + 28f(x) - 4x + 28x+45f(x) x + 147+45

Answer 1

The situation described is shown below:

Now, from this picture we notice that the area of the base of the large rectangle is:

$2x+9$

while its height is:

$2x+5$

The area then will be given as:

$\begin{gathered} f(x)=(2x+9)(2x+5) \\ =4x^2+10x+18x+45 \\ =4x^2+28x+45 \end{gathered}$

Therefore the function we are looking for is:

$f(x)=4x^2+28x+45$