An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is where s is in meters. Create a table of values and graph the function. Approximately what is the maximum height that the object will get?

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

From the information above, we can find out that

-4.9 t^2 + 19.6 t + 58.8 = 0

Completing the square will naturally put the equation into vertex form:

[tex]y=a(x-h)^2 + k[/tex]

where h will be the time it takes to get to a height of k.

Now,

[tex]-4.9 t^2 + 19.6 t + 58.8 = 0 \\\\-4.9 t^2 + 19.6 t = - 58.8 \\\\-4.9 (t^2 - 4t) = - 58.8[/tex]

Now take half the linear term, square it, and add it to both sides.

[tex]-4.9 (t^2 - 4t) = - 58.8 \\-4.9 (t^2 - 4t + 4) = - 58.8 - 19.6 \\\\-4.9 (t- 2) ^2= - 78.4[/tex]

[tex]s(t) = -4.9 (t- 2) ^2 + 78.4[/tex]

we see that the vertex is (2, 78.4).

The object reached its maximum height of 78.4 meters, the first choice is correct.

Learn more about vertex form of a quadratic equation here:

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