Solve Problems Using Systems in Three Variables
-You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the ball's height above the ground, y, after x seconds. Consider the following data: $$\begin{array} { c | c }
\begin{array} { c }
x , \text { seconds after } \
\text { ball is thrown }
\end{array} & \begin{array} { l }
y , \text { ball's height, in feet, } \
\text { above the ground }
\end{array} \
\hline 1 & 84 \
2 & 116 \
4 & 84
\end{array}$$ Find the quadratic function $y = a x ^ { 2 } + b x + c$ whose graph passes through the given points.
A) $y = - 16 x ^ { 2 } + 80 x + 20$
B) $y = - 12 x ^ { 2 } + 80 x + 16$
C) $y = - 16 x ^ { 2 } + 100 x + 0$
D) $y = - 10 x ^ { 2 } + 60 x + 34$

Question

Solve Problems Using Systems in Three Variables
-You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the ball's height above the ground, y, after x seconds. Consider the following data: $$\begin{array} { c | c } 
\begin{array} { c } 
x , \text { seconds after } \
\text { ball is thrown }
\end{array} & \begin{array} { l } 
y , \text { ball's height, in feet, } \
\text { above the ground }
\end{array} \
\hline 1 & 84 \
2 & 116 \
4 & 84
\end{array}$$ Find the quadratic function $y = a x ^ { 2 } + b x + c$ whose graph passes through the given points.
A) $y = - 16 x ^ { 2 } + 80 x + 20$
B) $y = - 12 x ^ { 2 } + 80 x + 16$
C) $y = - 16 x ^ { 2 } + 100 x + 0$
D) $y = - 10 x ^ { 2 } + 60 x + 34$

Quizplus · Accepted Answer

To find the correct quadratic function, we can substitute the given points into the general form $y = ax^2 + bx + c$ and solve the system of equations. For the point (1, 84), we get $a(1)^2 + b(1) + c = 84$, which simplifies to $a + b + c = 84$. For the point (2, 116), we get $a(2)^2 + b(2) + c = 116$, simplifying to $4a + 2b + c = 116$. For the point (4, 84), we get $a(4)^2 + b(4) + c = 84$, simplifying to $16a + 4b + c = 84$. Solving this system of equations yields $a = -16$, $b = 80$, and $c = 20$, which corresponds to the quadratic function $y = -16x^2 + 80x + 20$.

Solve Problems Using Systems in Three Variables -You Throw a Ball

Solve Problems Using Systems in Three Variables
-You Throw a Ball