story problems

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haliebre

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Sharon invest part of $12,000 @4% and the rest at 7%. If the annual income from these investments is $756 how much was invested at each rate?


Find the equation of the parabola that has the ordered pairs (1,1) (0.2) and (3,5) as points on the graph. Leave answer in the form y=ax2 +bx +c
 
I have tried to look in the book to see how I am supposed to set it up? but I am stumped.
 
haliebre said:
Sharon invest part of $12,000 @4% and the rest at 7%. If the annual income from these investments is $756 how much was invested at each rate?
Click to expand...
Did you WRITE DOWN useful definitions? It is ALWAYS an important FIRST step. Always!!!!

X = Amount Invested at 4%
Y = Amount Invested at 7% = $12,000 - X

I can see it all very clearly now. It was foggy before I wrote that.

Now what?
 
I suppose I have to put in a formula and solve for x and that is what I am struggling with
 
haliebre said:
Find the equation of the parabola that has the ordered pairs (1,1) (0.2) and (3,5) as points on the graph. Leave answer in the form y=ax2 +bx +c
Click to expand...
Plug the three (x, y)-points into the given parabola formula. Solve the resulting system of equation for "a", "b", and "c".

Your answer will be "y = ax<sup>2</sup> + bx + c" with those values plugged in.

Eliz.
 
haliebre said:
That is what I am confused about. How do I do that?
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How do you plug the given x-value in where the formula has an "x"...?

Just replace the "x" is the given value. For instance, if they'd given you the point (-3, -4), you would plug "-3" in for "x" and "-4" in for "y".

Eliz.
 
I am still not seeing how I will get the equation of the parabola when using those ordered pairs. I do not remember the professor covering this in class and the book isn't any help either.
 
haliebre said:
I am still not seeing how I will get the equation of the parabola when using those ordered pairs.
Click to expand...
Any parabola has an equation of the form "y = ax<sup>2</sup> + bx + c". Once you've solved for "a", "b", and "c", then you'll have the specific equation for this specific parabola.

Eliz.
 
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