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Sagot :
The given expression is equivalent to [tex]\rm -2(x-7)^2+118[/tex]price is $7 option first is correct.
What is a quadratic expression?
A quadratic expression is a second-degree algebraic expression represented by the:
[tex]\rm ax^2+bx+c=0[/tex] ........(1)
Where a, b, and c are the constants and
We have a quadratic expression:
[tex]\rm f(x)=-2x^2+28x+20[/tex]
Convert it to perfect square by perfect square trinomial:
[tex]\rm f(x)=-2(x^2+14x)+20[/tex]
[tex]\rm f(x)=-2(x^2+14x+49-49)+20[/tex] (adding and subtracting by 49)
[tex]\rm f(x)=-2(x-7)^2+2(49)+20[/tex]
[tex]\rm f(x)=-2(x-7)^2+118[/tex]
Here [tex]\rm (x-7)^2[/tex] is the positive term and -2 is the negative term so in order to get the highest weekly profit it should be zero, so
[tex]\rm -2(x-7)^2=0[/tex]
x = $7
Thus, the given expression is equivalent to [tex]\rm -2(x-7)^2+118[/tex] and the price is $7.
Learn more about quadratic expression here:
brainly.com/question/2263981
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