Answer:
y = -2x² + 7x - 11
Explanation:
To find the equation of a parabola that passes through the given points, we need to first determine the form of the equation.
A general form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants. To determine the values of a, b, and c, we substitute the coordinates of each point into the equation and solve the resulting system of equations.
Substituting the first point (-8, -309), we get:
-309 = a(-8)^2 + b(-8) + c
Substituting the second point (-5, -132), we get:
-132 = a(-5)^2 + b(-5) + c
Substituting the third point (1, 6), we get:
6 = a(1)^2 + b(1) + c
Substituting the fourth point (2, 1), we get:
1 = a(2)^2 + b(2) + c
Substituting the fifth point (6, -99), we get:
-99 = a(6)^2 + b(6) + c
Expanding the terms, we get a system of five equations:
64a - 8b + c = -309
25a - 5b + c = -132
a + b + c = 6
4a + 2b + c = 1
36a + 6b + c = -99
Solving the system of equations, we get:
a = -2
b = 7
c = -11
Therefore, the equation of the parabola that passes through the given points is:
y = -2x^2 + 7x - 11
So the answer is y = -2x² + 7x - 11. (^2 is just another version of ²)
Hope this helps!! I'm sorry if it's wrong. If you need more help, ask me! :]