SOLUTION: An athlete whose event is the shot put releases a shot whose path is shown by the graph to the right is released at an angle of 45°, its height, f(x), in feet, can be modeled by f

Question 1167170: An athlete whose event is the shot put releases a shot whose path is shown by the graph to the right is released at an angle of 45°, its height, f(x), in feet, can be modeled by f(x)= -0.02x^2 + 1.0x + 5.6, where x is the shot's horizontal distance, in feet, from its point of release
What is the shot's maximum horizontal distance, to the nearest tenth of a foot, or distance of the throw?
(I've tried using the quadratic formula to solve it but I cannot seem to get the decimal it wants.)
Answer by ikleyn(52791) (Show Source): You can put this solution on YOUR website!
.

The quadratic formula has nothing to do with this problem.

It is about finding the maximum of a quadratic function.

Solution

The maximum is where the VERTEX is.


The x-coordinate of the vertex is at  x = ,  where "a" is the coefficient at x^2 and "b" is the coefficient at x.


In your case,  a = -0.02,  b = 1.0,  so the x-coordinate of the vertex is


    x =  =  = 25.


Thus we just found the horizontal coordinate: the maximum will happen at x = 25 feet.


Now, to find the maximum height (y-coordinate), substitute x= 25 into the given formula for the height.

That's all.

---------------

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

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.

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Post-solution note

    Wording in your problem is terrible ---- TOOOOOOOO many EXCESSIVE UNNECESSARY words.

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