- #1

- 12

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err i have no idea hwo to do it except substituting those values in ... 0=9a+3b+c

what does it meant the family of quadratic functions?

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- Thread starter wellY--3
- Start date

- #1

- 12

- 0

err i have no idea hwo to do it except substituting those values in ... 0=9a+3b+c

what does it meant the family of quadratic functions?

- #2

- 184

- 0

b in terms of a and c

c in terms of a and b

then put them back into the original quadratic.

- #3

- 268

- 6

b in terms of a and c

c in terms of a and b

then put them back into the original quadratic.

From two equations, in general, you at most can eliminate only one of the unknowns. So from the original y=ax^2 +bx +c, you can remove only one of a or b or c.

Write, a in terms of b and c (or, b in terms of a and c; or, c in terms of a and b) and put in the original.... that is your family of equations for any choice of the existing two parameters.

- #4

- 12

- 0

what??

and put in the original what

and put in the original what

- #5

- 12

- 0

so c =-12x

is that right?

is that right?

- #6

uart

Science Advisor

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No, **c = -(9a + 3b)**.

So the family is,

[tex]y(x) = a x^2 + b x -(9a + 3b)[/tex]

The one given condition only lets you eliminate one unknown parameter. So you end up with a quadratic function that still has two free parameters, that's why it's referred to as a "family", there's lot of 'em. Get it?

So the family is,

[tex]y(x) = a x^2 + b x -(9a + 3b)[/tex]

The one given condition only lets you eliminate one unknown parameter. So you end up with a quadratic function that still has two free parameters, that's why it's referred to as a "family", there's lot of 'em. Get it?

Last edited:

- #7

HallsofIvy

Science Advisor

Homework Helper

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y= f(x)= ax

0= 9a+ 3b+ c so c= -(9a+3b). The answer to the question is that the family of all quadratic functions that pass through (3, 0) are those of the form f(x)= ax

(That's one way to write the answer: we could also, of course, have solved 9a+ 3b+ c= 0 for a, in terms of b and c, or for b, in terms of a and c, and replaced that parameter instead of c.)

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