Question
Answer
$$-0.00426(x-10.185)^2(x-17.928)^2+11.261=11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-0.00426(x-10.185)^2(x-17.928)^2+11.261& \xlongequal{ }-0.00426(x^2-20x+100)(x^2-34x+289)+11.261 \xlongequal{ } \\[1 em] & \xlongequal{ }-(0x^2+0x+0)(x^2-34x+289)+11.261 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-0+11.261 \xlongequal{ } \\[1 em] & \xlongequal{ }0+11 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}11\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{0x^20x0}\right) $ by each term in $ \left( x^2-34x+289\right) $. $$ \left( \color{blue}{0x^20x0}\right) \cdot \left( x^2-34x+289\right) = \\ = 0x^4 \cancel{0x^3} \cancel{0x^2} \cancel{0x^3} \cancel{0x^2} \cancel{0x} \cancel{0x^2} \cancel{0x}0 $$ |
| ② | Combine like terms: $$ 0x^4 \, \color{blue}{ \cancel{0x^3}} \, \, \color{green}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{blue}{ \cancel{0x^2}} \, \, \color{green}{ \cancel{0x}} \, \, \color{blue}{ \cancel{0x^2}} \, \, \color{green}{ \cancel{0x}} \,0 = 0 $$ |
| ③ | Combine like terms: $$ \color{blue}{0} + \color{blue}{11} = \color{blue}{11} $$ |
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