Find the equation $x=a t^{2}+b$ that fits the following data.

$\begin{array}{|l|l|l|l|l|l|l|}
\hline \mathrm{t}(\mathrm{sec})& 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{x}(\mathrm{m}) & -16 & -12 & 0 & 20 & 48 & 84 \
\hline
\end{array}$

A) $x=4 t^{2}-16$
B) $x=4 t^{2}+16$
C) $x=2 t^{2}+16$
D) $x=2 t^{2}-16$

Question

Find the equation $x=a t^{2}+b$ that fits the following data.

$\begin{array}{|l|l|l|l|l|l|l|}
\hline \mathrm{t}(\mathrm{sec})& 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{x}(\mathrm{m}) & -16 & -12 & 0 & 20 & 48 & 84 \
\hline
\end{array}$

A) $x=4 t^{2}-16$
B) $x=4 t^{2}+16$
C) $x=2 t^{2}+16$
D) $x=2 t^{2}-16$

Quizplus · Accepted Answer

To find the correct equation, we can substitute the values of $t$ and $x$ from the table into the equation $x=at^2+b$ and solve for $a$ and $b$. Using $t=0$ and $x=-16$, we get $-16=a(0)^2+b$, which simplifies to $b=-16$. Then, using $t=1$ and $x=-12$, we get $-12=a(1)^2-16$, which simplifies to $a=4$. Therefore, the equation is $x=4t^2-16$.

Find the Equation x=at2+bx=a t^{2}+bx=at2+b That Fits the Following Data A) x=4t2−16x=4 t^{2}-16x=4t2−16

Find the Equation $x=a t^{2}+b$ That Fits the Following Data A) $x=4 t^{2}-16$