Amuseum curator needs to frame a rectangular painting. the painting is 25 inches by 13 inches. if the frame has a width of x on all sides, what is the quadratic function that models the area of the painting and frame?

The quadratic function that models the area of the painting and frame is

Solution:

Given, A museum curator needs to frame a rectangular painting.  

The painting is 25 inches by 13 inches.  

The frame has a width of x on all sides,  

We have to find what is the quadratic function that models the area of the painting and frame

Now, we know that, dimensions of the painting and frame will be (25 + x + x) inches by (13 + x + x) inches

Because frame is x inches wide and it will add on both sides of painting

Then, area of painting and frame ⇒ length width

On solving we get,

Hence, the quadratic function is

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0