A rectangular picture measuring 3 in. by 5 in. is surrounded by a frame with uniform width x. How do you write a quadratic function in standard form to show the combined area of the picture and frame?

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Answer 1 · 2018-06-09T05:27:19

$y = 4 x^{2} + 16 x + 15$ $y=4x^2+16x+15$

Look at the diagram

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The outer length is $= 5 + 2 x$ $=5 +2x$
The outer width is $= 3 + 2 x$ $=3 +2x$

Let the area be $= y$ $=y$

Then-

$y = (5 + 2 x) (3 + 2 x)$ $y=(5+2x)(3+2x)$

$y = 15 + 6 x + 10 x + 4 x^{2}$ $y=15+6x+10x+4x^2$

$y = 4 x^{2} + 16 x + 15$ $y=4x^2+16x+15$