Standardized Test Practice
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At what point does the parabola have its maximum?
What is the first coordinate of the maximum height?
k=160
≈ 5.7 seconds
h= -4.9t^2+ 56t
Since the coefficient of t^2 is a negative number, the parabola will open downwards. Therefore, the maximum value of this equation will occur at the vertex.
The vertex of a parabola is the point (- b2 a,h(- b2 a)), where a and b are coefficients of t^2 and t. Let's substitute -4.9 for a and 56 for b to find the first coordinate of the vertex.
Substitute values
a(- b)=- a * b
Put minus sign in front of fraction
- (- a)=a
a/b=.a /1.4./.b /1.4.
Now we will find the maximum height by substituting the t-value of the vertex into the given equation.
t= 40/7
(a/b)^m=a^m/b^m
Calculate power
a*b/c= a* b/c
a/b=.a /4.9./.b /4.9.
a/b=.a /7./.b /7.
Multiply
Calculate quotient
Add terms
We found that the maximum height the rocket will reach is 160 meters.
In Part A we found that the point where the rocket's height has maximum value occurs at the vertex, ( 407,160). Since time is the first coordinate in this point, the rocket will reach its maximum height 407 seconds after it is launched. Let's use a calculator to write this number in decimal form.