Solve for variable

S

Sweetdaisy186

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Jan 21, 2005
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Hey guys!

I am so confused about this problem...a push in the right direction would be greatly appreciated! Thanks!

"A model for a valley between two mountains whose peaks touch the x-axis is y=40.4x^2-404x, where x and y are measured in feet. How deep is the valley?

I am confused because if I don't know one variable, how can I solve for the other one? I can't set the equation equal to itself right?

Any help would be greatly appreciated!

THANKS!
 
Sweetdaisy186 said:
Hey guys!

I am so confused about this problem...a push in the right direction would be greatly appreciated! Thanks!

"A model for a valley between two mountains whose peaks touch the x-axis is y=40.4x^2-404x, where x and y are measured in feet. How deep is the valley?

I am confused because if I don't know one variable, how can I solve for the other one? I can't set the equation equal to itself right?

Any help would be greatly appreciated!

THANKS!
Click to expand...

The equation
y = 40.4x<SUP>2</SUP> - 404x
has a graph which is a parabola. This parabola is a model for the valley, and the deepest point of the valley would be at the vertex of the parabola (the parabola opens upwards and its vertex is below the x-axis).

For a quadratic function of the form
y = ax<SUP>2</SUP> + bx + c
the x-coordinate of the vertex is -b/2a. To find the y-coordinate of the vertex, substitute -b/2a for x in the equation for the function.

In your equation, a = 40.4 and b = -404. Substitute into -b/2a to find the x-coordinate of the vertex. Then, use this as the value for x in the function and find y, which will be the depth of the valley.

I hope this helps you.
 
Hello, Sweetdaisy186!

A model for a valley between two mountains whose peaks touch the x-axis is: \(\displaystyle y\:=\:40.4x^2\,-\,404x\)
where \(\displaystyle x\) and \(\displaystyle y\) are measured in feet. How deep is the valley?
Click to expand...
You can graph the equation . . . or just imagine graphing it.

The graph is a parabola, opening upward.
The "depth" of the valley occurs at the vertex of the parabola.

And you know how to find the vertex, right?

[Edit: too fast for me, Mrspi!]
 
Oh yea! I remember that now. I totally forgot all about that. I understand it now! Thanks guys!
 
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