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Question: Given the function: \(f(x)=-3{{(x+2)}^{2}}+5\) , how do you rewrite in standard form?...

Given the function: f(x)=−3(x+2)2+5f(x)=-3{{(x+2)}^{2}}+5 , how do you rewrite in standard form?

Explanation

Solution

To solve the given problem one should know about the standard form of the polynomial equation, and to solve this problem we should remove all the brackets, once all the brackets are removed mathematically then it is said to be completed and we can get the general and standard form of the required polynomial equation given according to the standards.

Complete step-by-step answer:
We have, f(x)=−3(x+2)2+5f(x)=-3{{(x+2)}^{2}}+5
By expanding the equation using (a+b)2=a2+b2+2ab{{(a+b)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab , we get
f(x)=−3(x2+4x+4)+5 ⇒f(x)=−3x2−12x−12+5 ⇒f(x)=−3x2−12x−7 \begin{aligned} & f(x)=-3({{x}^{2}}+4x+4)+5 \\\ & \Rightarrow f(x)=-3{{x}^{2}}-12x-12+5 \\\ & \Rightarrow f(x)=-3{{x}^{2}}-12x-7 \\\ \end{aligned}
We have the general form of the quadratic equation to be like, f(x)=ax2+bx+cf(x)=a{{x}^{2}}+bx+c
The final equation by solving we got is similar as to the general form of quadratic equation, so we can say that the required form of the general or standard form of equation for this particular problem is f(x)=−3x2−12x−7f(x)=-3{{x}^{2}}-12x-7.

Note: The problem is solved by the above mentioned method, one should know about the general form of quadratic equations and the normal quadratic expansion formula, by applying those formulas only one get the solutions for the particular given problem, one may find difficulty if there is a negative sign in the expansion of the quadratic term and solving the exponents of the negative terms, one should carefully solve those in the given type of problems, or else there are chances of going wrong in the problem, once we remove all the brackets by expanding the terms, we will get the required standard form of solution.