Question

How do i find the vertex of the two rockets

Answer 1

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:

`h^2=-16t^2+150t+1`

To determine the coordinates of the vertex of this parabola you have to calculate the x-coordinate first, using the formula:

`x=-(b)/(2a)`

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

`\begin{gathered} t=-(150)/(2\cdot(-16)) \\ t=-(150)/(-32) \\ t=(75)/(16) \end{gathered}`

Replace the calculated value in the formula to determine the corresponding value of h:

`\begin{gathered} h=-16t^2+150t+1 \\ h=-16\cdot((75)/(16))^2+150\cdot(75)/(16)+1 \\ h=(5641)/(16) \\ h\approx352.56 \end{gathered}`

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.