Parabola question

Rengoku0510

New member
Hi, I would like to get some advice on this parabola question.

I thought it's one of the parabola and straight line questions but I can't apply my knowledge to this one... I got so confused and don't know where to start.

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Otis

Elite Member
Hi Rengoku. Could you be overthinking it?

The question does not concern the line, focus on the parabolic part.

You have a relationship given between x and y (containing the parameter: a).

Look for a pair of (x,y) coordinates that could help you determine the value of a.

If nothing else, experiment with the equation and numbers. I think you can do it!

Rengoku0510

New member
I thought the straight line is not part of the solution. But no matter how I played with the numbers I can't get the right answer 3300

lev888

Elite Member
I thought the straight line is not part of the solution. But no matter how I played with the numbers I can't get the right answer 3300
You have the equation. You are asked to find y at x=5. What do you get?

Rengoku0510

New member
I got 5. Still can't get to 3300...

lev888

Elite Member
I got 5. Still can't get to 3300...
R(x)=ax(6-x). Plug in x=5. What's the result?

Rengoku0510

New member
R(x)=ax(6-x). Plug in x=5. What's the result?

Harry_the_cat

Elite Member
You ignored the "a". You need to find "a" first.
Can you name a point (other than (6, 0)) that lies on the parabola? Read it off the graph.

Harry_the_cat

Elite Member
You ignored the "a". You need to find "a" first.
Can you name a point (other than (6, 0)) that lies on the parabola? Read it off the graph.
Use whole numbers.

lev888

Elite Member
Is it (3,6) and a=2?

Rengoku0510

New member
a is angle isn't it? So formula for angle is a=y/x so 6/3=2

lev888

Elite Member
a is angle isn't it? So formula for angle is a=y/x so 6/3=2
No, it's not an angle. Nowhere in the problem an angle is mentioned. a is an unknown constant that you need to find in order to calculate y at x=5.

Rengoku0510

New member
No, it's not an angle. Nowhere in the problem an angle is mentioned. a is an unknown constant that you need to find in order to calculate y at x=5.
I have no clue how to find a and I can't read it off the graph

lev888

Elite Member
I have no clue how to find a and I can't read it off the graph
R(x)=ax(6-x)
Given that you know exactly what the values of x and R(x) are at the point (3,6), what do you get when you plug in those values in the above? And can you then find a?

Harry_the_cat

Elite Member
Sub in x=3 and y=6 into y=ax(6-x) and solve for a.

Rengoku0510

New member
Sub in x=3 and y=6 into y=ax(6-x) and solve for a.
I got a=2/3. I still can't get to the answer I feel hopeless

Rengoku0510

New member
I managed to get the answer!!!
Sub a=2/3 and x=5 into y=ax(6-x). y=3.3 which is $3300. Can't believe I was struggling with such an easy question... Thank you for your help everyone Harry_the_cat Elite Member I managed to get the answer!!! Sub a=2/3 and x=5 into y=ax(6-x). y=3.3 which is$3300.

Can't believe I was struggling with such an easy question...
Thank you for your help everyone
Good on you for not giving up!!

Otis

Elite Member
Can't believe I was struggling with such an easy question
All humans struggle, until they've gained sufficient experience to encode and recognize patterns -- thus remembering what to do.

Here's a basic fact from algebra, to keep in mind regarding equations containing unknowns (symbols representing variables and/or parameters).

If you have only one equation, then it can be solved for only one of the symbols in terms of all the others.

In other words, if you desire to solve one equation to find some numerical result (like: "what sales level"), then you'll first need to obtain (and substitute) numerical values for all of the symbols but one.

And, anytime you're given a graph with an equation, look for points where the (x,y) values are evident. Both the graph and the equation define the same relationship between y and x, so graphs are a great resource for experimenting with equations because they provide values to substitute.

With practice, this all becomes automatic. Then, we struggle with the next concepts until they become encoded. Our math toolbox (brain) grows.