What is the equation, in standard form, of a parabola that contains the following points?
(2,0), (3,2), (4,6)
To find the equation of a parabola, we can use the standard form equation $y = ax^2 + bx + c$.
Plugging in the coordinates (2,0), (3,2), and (4,6) into this equation, we can create a system of three equations to solve for a, b, and c.
For the point (2,0):
$0 = 4a + 2b + c$
For the point (3,2):
$2 = 9a + 3b + c$
For the point (4,6):
$6 = 16a + 4b + c$
Now we have a system of three equations with three variables:
$4a + 2b + c = 0$
$9a + 3b + c = 2$
$16a + 4b + c = 6$
We can solve this system of equations to find the values of a, b, and c.