To determine which rocket flew higher, you have to determine the coordinates of the vertices of both parabolas and compare their y-coordinates.
Rocket 1
The path of this rocket is modeled by the quadratic formula:
[tex]h^2=-16t^2+150t+1[/tex]
To determine the coordinates of the vertex of this parabola you have to calculate the x-coordinate first, using the formula:
[tex]x=-\frac{b}{2a}[/tex]
Where
a is the coefficient of the quadratic term
b is the coefficient of the x-term
The variable that corresponds to "x" is the time in seconds "t"
The coefficients are a=-16 and b=150
[tex]\begin{gathered} t=-\frac{150}{2\cdot(-16)} \\ t=-\frac{150}{-32} \\ t=\frac{75}{16} \end{gathered}[/tex]
Replace the calculated value in the formula to determine the corresponding value of h:
[tex]\begin{gathered} h=-16t^2+150t+1 \\ h=-16\cdot(\frac{75}{16})^2+150\cdot\frac{75}{16}+1 \\ h=\frac{5641}{16} \\ h\approx352.56 \end{gathered}[/tex]
At the maximum point of the parabola (vertex), the height is approximately 352.56 feet
Rocket 2
To determine the coordinates of the vertex of the parabola described by the path of the second rocket you have to read the values directly for the graph.
On the x-axis are the values of the time, measured in seconds, and on the y-axis are the values of the height from the ground, measured in feet.
The coordinates are t = 6 and h ≈ 600.
This means that the highest point reached was at approximately 600 feet
Rocket 2 had a maximum height of approximately 600ft and rocket 1 reached an approximate height of 352.56ft. So, Rocket 2 flew higher.
