To find the standard form of the equation of a parabola, we can use the general equation:
y = ax^2 + bx + c
We can substitute the given points into this equation to set up a system of three equations.
1) For the point (0,1):
1 = a(0)^2 + b(0) + c
1 = 0 + 0 + c
c = 1
So, our equation becomes:
y = ax^2 + bx + 1
2) For the point (1,-3):
-3 = a(1)^2 + b(1) + 1
-3 = a + b + 1
3) For the point (-1,-9):
-9 = a(-1)^2 + b(-1) + 1
-9 = a - b + 1
Now we can solve this system of equations to find the values of a and b.
From equation (2):
a + b = -4 -> a = -4 - b
Substituting this value of a into equation (3):
-9 = (-4 - b) - b + 1
-9 = -8 - 2b
2b = -1
b = -1/2
Now we can substitute the value of b back into equation (2):
a - 1/2 = -4
a = -4 + 1/2
a = -7/2
Therefore, the equation of the parabola in standard form is:
y = (-7/2)x^2 - (1/2)x + 1
Write the equation in standard form of the parabola containg the following point (0,1) (1,-3) (-1,-9)
set up a system of three equations
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