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. Â
The painting is 25 inches by 13 inches. Â
The frame has a width of x on all sides, Â
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 [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]
