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Oirection:
Math-AlgCBAv22 (copy)
28
Alicia completed the square in the quadratic function
p(x)=-2x^(2)+24 x-67 in order to determine the maximum value of
p(x). The new form of the function that resulted from her work was
p(x)=-2(x-6)^(2)+◻
What number should go in the box so that Alicia's new form is equivalent to the original form of
p(x) ? Enter the answer as an integer or a decimal in the box.

p(x)=-2(x-6)^(2)+◻

Oirection: $\newline$ Math-AlgCBAv $22$ (copy) $\newline$ $28$ $\newline$ Alicia completed the square in the quadratic function $p(x)=-2 x^{2}+24 x-67$ in order to determine the maximum value of $p(x)$ . The new form of the function that resulted from her work was $p(x)=-2(x-6)^{2}+\square$ $\newline$ What number should go in the box so that Alicia's new form is equivalent to the original form of $p(x)$ ? Enter the answer as an integer or a decimal in the box. $\newline$ $p(x)=-2(x-6)^{2}+\square$

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Find derivatives of other trigonometric functions

Full solution

Q. Oirection:

\newline

Math-AlgCBAv

22

(copy)

\newline

28

\newline

Alicia completed the square in the quadratic function

p(x)=-2 x^{2}+24 x-67

in order to determine the maximum value of

p(x)

. The new form of the function that resulted from her work was

p(x)=-2(x-6)^{2}+\square

\newline

What number should go in the box so that Alicia's new form is equivalent to the original form of

p(x)

? Enter the answer as an integer or a decimal in the box.

\newline

p(x)=-2(x-6)^{2}+\square

Calculate square of $x-6$ : Calculate the square of $(x-6)$ to see what we get when we expand $-2(x-6)^2$ . $\newline$ $(x-6)^2 = x^2 - 12x + 36$
Multiply expanded form by $-2$ : Multiply the expanded form by $-2$ to match the coefficient of the $x^2$ term in the original equation. $\newline$ $-2(x^2 - 12x + 36) = -2x^2 + 24x - 72$
Compare constant terms: Compare the constant term of the expanded form with the original equation. $\newline$ Original constant term: $-67$ $\newline$ Expanded constant term after multiplying by $-2$ : $-72$
Find the difference: Find the difference between the original constant term and the expanded constant term. $\newline$ Difference: $-67 - (-72) = -67 + 72 = 5$
Add difference to expanded form: Add the difference to the expanded form to get the equivalent form. $p(x) = -2(x-6)^2 + 5$

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