I'm having some trouble with these, so any help is appreciated! The directions are to write the equation in standard form for the parabola that passes through the points
1. ( -6, 0), (-3, 3), and (-4, 0)
2. (-1, 2), (4, -23), and (2, -7)
3. (-4, 9), (0, -7), and (1, -1)
1. ( -6, 0), (-3, 3), and (-4, 0)
2. (-1, 2), (4, -23), and (2, -7)
3. (-4, 9), (0, -7), and (1, -1)
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The equation for a parabola can be written ax² + bx + c = y.
Plug in the coordinates from each of the three points.
(-3, 3): 9a - 3b + c = 3
(-4, 0): 16a - 4b + c = 0
(-6, 0): 36a - 6b + c = 0
Now take this system of three equations and solve for a, b, and c.
I hope you know how to do that, because it is too hard to explain clearly here, but the solution is
a = 1
b = 10
c = 24
The equation of the parabola becomes x² + 10x + 24 = y
Plug in the coordinates from each of the three points.
(-3, 3): 9a - 3b + c = 3
(-4, 0): 16a - 4b + c = 0
(-6, 0): 36a - 6b + c = 0
Now take this system of three equations and solve for a, b, and c.
I hope you know how to do that, because it is too hard to explain clearly here, but the solution is
a = 1
b = 10
c = 24
The equation of the parabola becomes x² + 10x + 24 = y