Question

Write an equation of the parabola that passes through the point (-9, 6) and has a vertex (5, 1). use the variables x and y. an equation of the parabola is y =

Answer 1

To find the equation of the parabola, you need to substitute the coordinates of the given point and the vertex into the general form of a parabola equation and solve the resulting system of equations.

Step-by-step explanation:

The equation of a parabola that passes through the point (-9, 6) and has a vertex (5, 1) can be found using the general form of a parabola equation, which is y = ax^2 + bx + c.

First, substitute the coordinates of the vertex into the equation to find the value of 'a':

1 = a(5)^2 + b(5) + c

1 = 25a + 5b + c

Next, substitute the coordinates of the given point into the equation to find another equation:

6 = a(-9)^2 + b(-9) + c

6 = 81a - 9b + c

You now have a system of three equations with three unknowns (a, b, c). Solve this system of equations to find the values of a, b, and c, and then substitute them back into the general equation to obtain the equation of the parabola.