Quadratic Problem

calico

New member
Joined
Nov 10, 2010
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Here is the question:

The path of a flying disk can be modeled by the relation

h= -0.0625d(d - 112)

Where h = the height, in metres above the ground
and d = the horizontal distance, in metres

- - - - -

a) At what horizontal distance does the disk lay on the ground?

b) At what horizontal distance does the disc reach its maximum height

c) What is the maximum height?


Alright, so I understand that the horizontal distance is somewhere on the X axis, and vertical distance on the Y axis,
but how do you solve the questions using that?

Thanks in advance!
 
calico said:
a) At what horizontal distance does the disk lay on the ground?

When the disk is on the ground, its height above the ground is zero meters.

In other words, they want you to find d when h = 0.

Substitute the number 0 for h, and use algebra to solve the resulting equation for d.


b) At what horizontal distance does the disc reach its maximum height

This asks for the d-coordinate of the vertex point. (They're calling the x-axis the d-axis, in this exercise.)

There's a formula for calculating the d-coordinate of the vertex point, using the coefficients.

After you multiply out (expand) the given expression for h, you'll have a quadratic polynomial of this form:

h = Ad^2 + Bd

where A and B are the coefficients.

The formula for the horizontal coordinate of the vertex point is -B(2A).


EG: Find the x-coordinate of the vertex point:

y = 4x^2 - 7x

A is 4 and B is -7, so the x-coordinate at the vertex is:

-B/(2A) = -(-7)/(2*4) = 7/8


c) What is the maximum height?

This is the vertical coordinate of the vertex. Find it by substitution.

EG:

Using the example above, we substitute x = 7/8 into the expression for y.

y = 4x^2 - 7x

4(7/8)^2 - 7(7/8) = -63/16

The vertex coordinates are (7/8, -63/16).

If you want more detailed help, you'll need to share your work, so that we can see where you're stuck.

If I wrote anything that you don't understand, please ask specific questions. I can't know what you've already learned about quadratic polynomials and equations, until you tell me.

Cheers ~ Mark

 
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