The equation of a parabola in standard form is given by: y = ax^2 + bx + c.
We can set up a system of three equations using the given points:
1) (0, 1): 1 = a(0)^2 + b(0) + c, which simplifies to: 1 = c.
2) (1, -3): -3 = a(1)^2 + b(1) + c, which simplifies to: -3 = a + b + 1.
3) (-1, -9): -9 = a(-1)^2 + b(-1) + c, which simplifies to: -9 = a - b + 1.
From equation 1, we know that c = 1. Substituting this value into equations 2 and 3, we get:
-3 = a + b + 1,
-9 = a - b + 1.
Subtracting the second equation from the first, we eliminate a: 6 = 2b, which simplifies to: b = 3.
Substituting this value back into equation 2, we get: -3 = a + 3 + 1,
-3 = a + 4,
a = -7.
Therefore, the equation of the parabola is: y = -7x^2 + 3x + 1.
Write the equation, in standard form, of the parabola containing the following points: (0, 1), (1, -3), (-1, -9). You must set up a system of three equations in your work in order to get full credit for this question. (1 point) show all of your work
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