need help finding x,y + few hw problems! (parabolas etc)

[fiercey]

I just need clarification for the answer to this system of equations...

(6x)+(5y)=(-3)
(-x)-(5/6y)=(-7)

I multiplied the second equation by 6, which eliminated both X and Y, then got: 0=-45... so should the answer be "no real solution"?

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find the equation of a parabola with the points
(1,3)(2,2)(3,-3)

could anyone help me with this?

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Also, how do I sketch this on a graph: x^2+(y-2)^2 <= 9

thanks in advanced, im new to this board and i hope to be a help in the future!

 

[galactus]

find the equation of a parabola with the points
(1,3)(2,2)(3,-3)

could anyone help me with this?

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Use the equation for a parabola:

\(\displaystyle ax^{2}+bx+c\)

Use three of them, enter in your respective x values and set them to the respective y values. You'll have a system of three equations in three unknowns, (a,b,c). Solve the system for a,b,c.

 

[soroban]

Hello, fiercey!

Welcome aboard!

\(\displaystyle \;6x\,+\,5y\:=\:-3\)
\(\displaystyle \,-x\,-\,\frac{5}{6}y\:=\:-7\)

I multiplied the second equation by 6, which eliminated both x and y, then got: \(\displaystyle \0\,=\,-45\)
. . . so should the answer be "no real solution"? . . . Yes!

Find the equation of a parabola with the points: (1,3), (2,2), (3,-3)

As Galactus suggested, we have a quadratic function: \(\displaystyle \,y\:=\;ax^2\,+\,bx\,+\,c\)

We need to determine the three coefficents: a, b, c.
And we know three points ... values that satisfy the function.

\(\displaystyle (1,3):\;\;3\;=\;a\cdot1^2\,+\,b\cdot1\,+\,c\;\;\Rightarrow\;\;a\,+\,b\,+\,c\:=\:3\)

\(\displaystyle (2,2):\;\;2\;=\;a\cdot2^2\,+\,b\cdot2\,+\,c\;\;\Rightarrow\;\;4a\,+\,2b\,+\,c\:=\:2\)

\(\displaystyle (3,\)-\(\displaystyle 3):\;\)-\(\displaystyle 3\;=\;a(\)-\(\displaystyle 3)^2\,+\,b(\)-\(\displaystyle 3)\,+\,c\;\;\Rightarrow\;\;9a\,-\,3b\,+\,c\:=\:-3\)

Now solve this system of equations.

How do I sketch this on a graph: \(\displaystyle \,x^2\,+\,(y\,-\,2)^2\;\leq\;9\)

The equation: \(\displaystyle \,x^2\,+\,(y\,-\,2)^2\;=\;9\,\) is a circle with center (0,2) and radius 3.
\(\displaystyle \;\;\)Graph that.

The "less than" means we want the points in the interior of the circle.
\(\displaystyle \;\;\)Shade the interior of the circle.

The graph is the set of points inside and on the circle.

 

[Denis]

I just need clarification for the answer to this system of equations...
(6x)+(5y)=(-3)
(-x)-(5/6y)=(-7)

Check your 2nd equation: could it be -x + (5/6y) = -7 ?

Btw, preferable to type (5/6y) this way: 5y/6