Word Problem - A football player kicks a ball...

I

ILovePizza

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A football player kicks a ball into the air. The ball’s path can be modeled by the relation:
h = -0.04(d – 19)^2 + 14.44

Where h is the ball’s height and d is the ball’s distance from the kicker, both in metres.

QUESTIONS

A) What is the ball’s maximum height reached by the ball?
B) Express the relation in standard form and in intercept form.
C) What horizontal distance will the ball travel before it lands?
D) The goalposts are 35m away and the crossbar is approximately 3m high. Will the ball clear the crossbar?

I’m terrible at these questions, and not sure how to approach or set-up to solve these questions.
If someone could provide guidance for this example, I can use it as a template for my school problems, which I have several similar to this one.
Thank you.
 
You are given a negative quadratic, which graphs as an upside-down parabola. The vertex then is the maximum height, with the x-value at the vertex being the maximizing value of the input variable.

a) Find the y-coordinate of the vertex.

b) You'll have to check for your book's definitions of "standard" and "intercept" forms.

c) What is the height, above the ground, when the ball is on the ground? Plug this value in for "h", and solve for the time "t". Only one of the solutions will make sense in context.

d) What is the horizontal distance covered when the height is h = 3?

If you get stuck, please reply showing your work and reasoning so far. Thank you! :D
 
I tried to enter the following for my graph, but it wont work:

-0.04(d – 19)^2 + 14.44

This is the problem, I'm note sure how to format the numbers to get the results.

The standard form example in the book looks like this:

y=(x+6)^2
_=(x+6)(x+6)
_=x^2+6x+6x+36
_=x^2+12x+36

The intercept form shown: y=a(x-r)(x-s)
 
What are you "entering", where?

Where are you having trouble with what the exercise has asked you to do?

Please be complete. Thank you! :D
 
I’m having trouble with all of it: I have being so much math lately, I feel I’ve hit a wall, and I am just unable to process the problem.
It’s like my brain has just locked frozen, and I can’t seem to get this problem.
I entered Y=-0.04(d – 19)^2 + 14.44, into my calculator, trying to graph the results, but that obviously did not get me very far…I know I need a break, but I have several similar questions, and thought if someone could provide a solid example, it would re-start my brain, so I can do the others.

I can’t be the only one who hit a wall in math before? Sorry just tired.
Bottom line – I’m not sure what to do anymore…too much too fast, too tired, and I can’t process it all.
 
ILovePizza said:
A football player kicks a ball into the air. The ball’s path can be modeled by the relation:
h = -0.04(d – 19)^2 + 14.44

Where h is the ball’s height and d is the ball’s distance from the kicker, both in metres.d
QUESTIONS

A) What is the ball’s maximum height reached by the ball?
B) Express the relation in standard form and in intercept form.
C) What horizontal distance will the ball travel before it lands?
D) The goalposts are 35m away and the crossbar is approximately 3m high. Will the ball clear the crossbar?

I’m terrible at these questions, and not sure how to approach or set-up to solve these questions.
If someone could provide guidance for this example, I can use it as a template for my school problems, which I have several similar to this one.
Thank you.
Click to expand...

You may need to review some BASICS about quadratic functions.

If you have a function f(x) = a(x - h)^2 + k

When a function is in THIS form, the vertex (maximum or minimum) point is at (h, k)...."k" is the max or minimum value of the function.

Then the VERTEX of this function is at (h, k). The vertex of a quadratic function represents the maximum value for the function if a < 0, and it represents the minimum value of the function of a > 0.

Your problem gives "h" as a function of "d"

Compare your equation to the standard form:
f(x) = a(x - h)^2 + k
h = -0.04(d - 19)[sup:bo2gvq88]2[/sup:bo2gvq88] + 14.44

Looks like h is 19, and k is 14.44

That means the maximum value of the function happens when d = 19, and h = 14.44.....

STANDARD FORM, as defined in MOST textbooks is

f(x) = ax^2 + bx + c

Take your equation:

h = -0.04(d - 19)[sup:bo2gvq88]2[/sup:bo2gvq88] + 14.44

To get this in standard form, DO the multiplication, and combine like terms:

h = -0.04(d - 19)(d - 19) + 14.44

Multiply out (d - 19)(d - 19)....then multiply the result by -0.04. Then combine like terms to simplify the expression, and you should end up with STANDARD FORM.

I'll leave "intercept form" to you....

Please show us what you've tried, so we can see where you need help.
 
Sorry for the delay in answering, but I've been reviewing this math course, and have decided to quit. Algebra, is not for everyone; I don't understand it, and despite the past month, or so of doing it, it's just not making any more sense...no headway at all. In fact, it's more confusing now, than when I first started.

I do appreciate all your help.
Thanks!
 
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