Answer:

or

Step-by-step explanation:
we have
f(3+√2 )=f(3− √2 )=0
so
x1=3+√2 and x2=3−√2 are the roots or x-intercepts of the quadratic equation
The quadratic equation in factored form is equal to

substitute

Find the value of the coefficient a
Remember that
f(1)=−8
so
For x=-1 -----> f(x)=-8
substitute

solve for a

apply difference of squares


therefore


simplify
Applying distributive property


A translation by 11 units to the left and 3 units up
Total height of lumber, H = 10 1/2 feet = 21/2 feet .
Height of side panel, h = 5 2/3 feet = 17/3 feet .
Now,
Extra lumber required, L = 2 × Height of side panel - Total height of lumber
![L=[2\times (\dfrac{17}{3})]-\dfrac{21}{2}\\\\L = \dfrac{5}{6}\ feet](https://tex.z-dn.net/?f=L%3D%5B2%5Ctimes%20%28%5Cdfrac%7B17%7D%7B3%7D%29%5D-%5Cdfrac%7B21%7D%7B2%7D%5C%5C%5C%5CL%20%3D%20%5Cdfrac%7B5%7D%7B6%7D%5C%20feet)
Therefore, extra lumber required is
feet.
Hence, this is the required solution.