Any of you know how to do this?

[Curd]

I don't even know where to begin with this one. I thought that simplifying the first equation my help but I really doubt that now. And this is from an algebra book.

 

[hotvette]

You have an equation of a parabola and 3 points. From this you can find expressions for a, b, and c in terms of h, y₀, y₁, and y₂. Substituting the values for a and c into the first equation will yield the second equation. Hint: you don't even need to solve for b.

 

[Curd]

You have an equation of a parabola and 3 points. From this you can find expressions for a, b, and c. Substituting the values for a and c into the first equation will yield the second equation.

so i was right? i just need to change the first equation into ax squared+ bx + c form?

 

[Mentallic]

so i was right? i just need to change the first equation into ax squared+ bx + c form?

I'm not quite sure what you mean by that, and I have a feeling the answer is no

Substitute the values (h,y₂) and (-h,y₀) into the general quadratic equation. Can you see a way of getting rid of the "b"?

 

[Mark44]

In addition to what hotvette and Mentallic said, the problem is equivalent to showing that 2ah² + 6c = y₀ + 4y₁ + y₂.

Use the formula for the parabola and the three points that are given to find y₀, y₁, and y₂, and then show that the equation above follows.

 

[Curd]

In addition to what hotvette and Mentallic said, the problem is equivalent to showing that 2ah² + 6c = y₀ + 4y₁ + y₂.

Use the formula for the parabola and the three points that are given to find y₀, y₁, and y₂, and then show that the equation above follows.

the whole stupid thing was just a substitution issue? ( y of -h for y2, y of 0 for y1 and y of h for y2)

how do you know to substitute?

 

[Mark44]

the whole stupid thing was just a substitution issue? ( y of -h for y2, y of 0 for y1 and y of h for y2)

how do you know to substitute?

It's probably the most obvious thing to start with.

You're given:
1) the equation of the parabola: y = ax² + bx + c
2) three points on the graph of this parabola: (-h, y₀), (0, y₁), and (h, y₂)
3) A formula for the area between the x-axis and the parabola, between x = -h and x = h: A = (h/3)(2ah² + 6c)

You're asked to show that the expression for area above can be written in another expression that involves y₀, y₁, and y₂.

A natural thing to try would be to substitute the three given points into the equation for the parabola, and see what happens when you do that.

 

[Curd]

It's probably the most obvious thing to start with.

You're given:
1) the equation of the parabola: y = ax² + bx + c
2) three points on the graph of this parabola: (-h, y₀), (0, y₁), and (h, y₂)
3) A formula for the area between the x-axis and the parabola, between x = -h and x = h: A = (h/3)(2ah² + 6c)

You're asked to show that the expression for area above can be written in another expression that involves y₀, y₁, and y₂.

A natural thing to try would be to substitute the three given points into the equation for the parabola, and see what happens when you do that.

didn't seem real natural to me. i wish they would have explained the problem a bit better.

 

[Mark44]

didn't seem real natural to me. i wish they would have explained the problem a bit better.

On the other hand, part of these kinds of problems is to take the information that is given, and figure out what you need to do with it to arrive at the solution.

 

[Curd]

On the other hand, part of these kinds of problems is to take the information that is given, and figure out what you need to do with it to arrive at the solution.

I tend to expect such a thing to be true of the problem that is represented by the language of mathematics, but not to be true of the language itself.

in other words, this problem was an issue of understanding their jargon, for lack of a better word than jargon at the moment, rather than a mathematical concept. When I'm presented with a problem i tend to expect it to be about understanding a mathematical concept and not the particular jargon used.

this wasn't even an issue of understand a relationship between equations. it was more of an issue of understanding the relationship of the notations they were using. it was kind of a cheap shot on their part.

 

[Mark44]

I tend to expect such a thing to be true of the problem that is represented by the language of mathematics, but not to be true of the language itself.

in other words, this problem was an issue of understanding their jargon, for lack of a better word than jargon at the moment, rather than a mathematical concept. When I'm presented with a problem i tend to expect it to be about understanding a mathematical concept and not the particular jargon used.

What jargon? The language that was used seemed to me to be ordinary, simple English. Can you give an example of what you considered to be jargon?

this wasn't even an issue of understand a relationship between equations. it was more of an issue of understanding the relationship of the notations they were using. it was kind of a cheap shot on their part.

What notations are you talking about?

 

[Curd]

What jargon? The language that was used seemed to me to be ordinary, simple English. Can you give an example of what you considered to be jargon?
What notations are you talking about?

they used y0 to mean y of -h or y(-h) or f of -h or f(-h)... however you wish to write it.

they used y1 to mean y of 0 or y(0) or f of 0 or f(0)... however you wish to write it.

they used y2 to mean y of h or y(h) or f of h or f(h)... however you wish to write it.

the fact that realizing that was the crux of the problem, even to the point of being the problem itself means that this problem was not about math but about figuring out what they meant when they used the "jargon, for lack of a better term, y1 y0 and y2.

i've never seen y's used like that before.

had they written it as

A= h/3 ( f(-h) + f(0) + f(h) )


it would have made much more sense.

 

[hotvette]

To Curd,

This is basic problem solving and is quite typical of what students will frequently be expected to solve. It's meant to challenge your thinking and use your fundamental understanding of math to help solve it. It's a learned skill. You'll get a lot more like it. In this particular case, the logic to arrive at the answer might look like:

1. What is the objective? Ans: show that equation 1 can be made to look like equation 2

2. Analyze equation 1 and equation 2. Notice that equation 1 has a & c but equation 2 has y₀, y₁, y₂

3. How do I turn a & c into expressions involving y₀, y₁, y₂?

4. See what other information is provided that might be useful. Ah, I'm given 3 points and am told the three points are on a parabola

5. Ah ha moment. I know from fundamental understanding of parabolas that I can use the 3 points to solve for a, b, c

6. Use the solution of #5 to answer the question in #3. Substitute into equation 1 and simplify.

 

[Mark44]

they used y0 to mean y of -h or y(-h) or f of -h or f(-h)... however you wish to write it.

they used y1 to mean y of 0 or y(0) or f of 0 or f(0)... however you wish to write it.

they used y2 to mean y of h or y(h) or f of h or f(h)... however you wish to write it.

This is not jargon. All they are doing here is using subscripts to identify three different y values. You can see from the graph in the problem statement that these are three different y values.

The equation of the parabola was not defined in function notation, meaning it was not defined as f(x) = ax² + bx + c, so f(-h), f(0), and f(h) would not be meaningful in this problem.

the fact that realizing that was the crux of the problem, even to the point of being the problem itself means that this problem was not about math but about figuring out what they meant when they used the "jargon, for lack of a better term, y1 y0 and y2.

i've never seen y's used like that before.

had they written it as

A= h/3 ( f(-h) + f(0) + f(h) )

As already noted, since they didn't define a function f, it would have been meaningless to talk about values of a function that hadn't been defined.

it would have made much more sense.

 

[Curd]

This is not jargon. All they are doing here is using subscripts to identify three different y values. You can see from the graph in the problem statement that these are three different y values.

The equation of the parabola was not defined in function notation, meaning it was not defined as f(x) = ax² + bx + c, so f(-h), f(0), and f(h) would not be meaningful in this problem.
As already noted, since they didn't define a function f, it would have been meaningless to talk about values of a function that hadn't been defined.

acutally, they did define the function of f. they say plain as day that the graph is of
y= ax squared + bx + c

sorry, i didn't get what you said at first.

this reminds me of way back when i always rewrote f(x) as y. so the whole issue was that i didn't realize that we were replacing f(x) with y, right?

 

[Mark44]

acutally, they did define the function of f. they say plain as day that the graph is of
y= ax squared + bx + c

Actually, they didn't define any function f. If they had, what you posted would have said f(x) = ax² + bx + c. Certainly y is a function of x, as shown in this equation, but there is no mention of a function named f or g or any of the letters usually used for function names.

sorry, i didn't get what you said at first.

this reminds me of way back when i always rewrote f(x) as y. so the whole issue was that i didn't realize that we were replacing f(x) with y, right?

What do you do when you are given an equation such as t = f(y)?

 

[Curd]

Actually, they didn't define any function f. If they had, what you posted would have said f(x) = ax² + bx + c. Certainly y is a function of x, as shown in this equation, but there is no mention of a function named f or g or any of the letters usually used for function names.

What do you do when you are given an equation such as t = f(y)?

go find the equation f. then plug y into it to see if i can get t?

 

[Mark44]

What do you do when you are given an equation such as t = f(y)?

go find the equation f. then plug y into it to see if i can get t?

You said earlier that, whenever you used to see f(x), you replaced it with y. What I meant by this question was, what do you replace f(y) with?

Where I was going with this was to caution you about doing too many things on autopilot, without thinking.

 

[Curd]

You said earlier that, whenever you used to see f(x), you replaced it with y. What I meant by this question was, what do you replace f(y) with?

Where I was going with this was to caution you about doing too many things on autopilot, without thinking.

i think i would need more context to understand your hypothetical situation.

maybe i should stop typing about this for a night or two. everything always makes more sense the next day..