A museum 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 [tex]4 x^{2}+76 x+325[/tex]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 frameNow, 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 [tex]\times[/tex] width[tex]\rightarrow(13+2 x) \times(25+2 x)[/tex]On solving we get,[tex]\begin{array}{l}{\rightarrow 13(25+2 x)+2 x(25+2 x)} \\\\ {\rightarrow 325+26 x+50 x+4 x^{2}} \\\\ {\rightarrow 4 x^{2}+76 x+325}\end{array}[/tex]Hence, the quadratic function is [tex]4 x^{2}+76 x+325[/tex]