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Re-write the quadratic function below in Standard Form

y=6(x-1)^(2)+2
Answer:
y=

Re-write the quadratic function below in Standard Form $\newline$ $y=6(x-1)^{2}+2$ $\newline$ Answer: $y=$

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Write a quadratic function from its zeros

Full solution

Q. Re-write the quadratic function below in Standard Form

\newline

y=6(x-1)^{2}+2

\newline

Answer:

y=

Expand squared term: Expand the squared term. $\newline$ We need to expand the term $(x-1)^2$ to rewrite the quadratic function in standard form. $\newline$ Using the identity $(a-b)^2 = a^2 - 2ab + b^2$ , we get: $\newline$ $(x-1)^2 = x^2 - 2(x)(1) + 1^2$ $\newline$ $(x-1)^2 = x^2 - 2x + 1$
Multiply expanded term: Multiply the expanded term by the coefficient. $\newline$ The expanded term $x^2 - 2x + 1$ needs to be multiplied by the coefficient $6$ . $\newline$ $y = 6(x^2 - 2x + 1)$ $\newline$ Distribute the $6$ to each term inside the parentheses: $\newline$ $y = 6x^2 - 12x + 6$
Add constant term: Add the constant term to the expression. $\newline$ The constant term outside the parentheses is + $2$ , so we add it to the expression we obtained in Step $2$ . $\newline$ $y = 6x^2 - 12x + 6 + 2$ $\newline$ Combine like terms: $\newline$ $y = 6x^2 - 12x + 8$

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