# Math Help - Finding equation for quad function with given 3 points

1. ## Finding equation for quad function with given 3 points

Find an equation for the quadratic function whose graph contains the points (-6,3), (1,-32), and (-4,3).

I have many problems similar to this but I don't know how to set it up. Help would be great =]

2. Originally Posted by Kitty216
Find an equation for the quadratic function whose graph contains the points (-6,3), (1,-32), and (-4,3).

I have many problems similar to this but I don't know how to set it up. Help would be great =]
All quadratics can be written in the form

$y = ax^2 + bx + c$.

By substituting the three points, you end up with three equations in three unknowns that you can solve simultaneously.

$3 = a(-6)^2 + b(-6) + c$

$-32 = a(1)^2 + b(1) + c$

$3 = a(-4)^2 + b(-4) + c$

3. Originally Posted by Kitty216
Find an equation for the quadratic function whose graph contains the points (-6,3), (1,-32), and (-4,3).

I have many problems similar to this but I don't know how to set it up. Help would be great =]
$y = ax^2 + bx + c$

$3 = a(-6)^2 + b(-6) + c$

$-32 = a(1)^2 + b(1) + c$

$3 = a(-4)^2 + b(-4) + c$

solve the system for the coefficients $a$, $b$, and $c$.

4. oh I see. Thanks guys!!

Out of curiosity, what form of equation would be used if the 3 points were on a circle?

5. Originally Posted by Kitty216
oh I see. Thanks guys!!

Out of curiosity, what form of equation would be used if the 3 points were on a circle?
Then it would be

$(x - h)^2 + (y - k)^2 = r^2$

where $(h, k)$ is the co-ordinate of the centre and $r$ is the radius.

If you have three points, once again you will get three equations in three unknowns.

6. oh ok! Thank you for the help!