Nicky wants to surround a painting 5 inches by 11 inches with a frame that is w inches wide. Write a quadratic function A in standard form to represent the combined area A of the picture and the frame. A(w) = w2 + w +

Since the frame is uniform around the picture, you need to add its width, W, to the sides of the picture. We will manipulate the formula for area, A = L x W. To ease confusion with the chosen variable, I will replace the W with an H for height to be A = L x H.

L = W + 11 + W

H = W + 5 + W

You can see this by drawing a picture with a frame around it. Looking from the top to the bottom, you will have it's width plus the picture plus the width of the frame again. Same thing for the height of the picture. Looking from the far left of the frame and across, you have the width of the frame plus the picture plus the width of the frame again. Now plug these into the area formula and combine like terms.

A = L x H

A = (W + 11 + W) x (W + 5 +W)

A = (2W + 11) x (2W + 5)

Now take the product of the two parenthesis.

I learned to use the FOIL method: multiply First, Outside, Inside, Last.

A = (2W x 2W) + (2W x 5) + (11 x 2W) + (11 x 5)

A = 4W2 + 10W + 22W + 55

A = 4W2 + 32W + 55

Step-by-step explanation:

A(w)=4w^2+32w+55

Step-by-step explanation: