SOLUTION: Travis and Laura are rock climbing. Travis throws a spike to Laura. The function h(t)=-5t^2+20t+110 models he height of the spike in metres above the ground at time t. Laura is 135

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Travis and Laura are rock climbing. Travis throws a spike to Laura. The function h(t)=-5t^2+20t+110 models he height of the spike in metres above the ground at time t. Laura is 135      Log On


   

Question 1137554: Travis and Laura are rock climbing. Travis throws a spike to Laura. The function h(t)=-5t^2+20t+110 models he height of the spike in metres above the ground at time t. Laura is 135 m above the ground. Did Travis’ throw reach Laura? Explain your answer.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is about the maximum value of a quadratic function.


The quadratic function  f(x) = ax^2 + bx + c  of the general form with the negative leading coefficient  a < 0

has the maximum value at  x = -b%2F%282a%29.


In this case, the maximum height is achieved at  t = -20%2F%282%2A%28-5%29%29 = %28-20%29%2F%28-10%29 = 2 seconds.    ANSWER


The maximum height the spike will achieve is equal to the value of the given function  h(t) at t= 2 :


    h%5Bmax%5D = -5%2A2%5E2+%2B+20%2A2+%2B+110 = -20 + 40 + 110 = 130 meters.  

    Hence, it will not achieve Laura.        ANSWER

Answered, explained and solved.

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On finding the maximum/minimum of a quadratic function see the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.