Final answer:
The question is about finding the equation of a parabola that is parallel to the x-axis and passes through three given points. The general form of such a parabola is x = ay^2 + by + c, and by using the given points, we can solve for coefficients a, b, and c to determine the specific equation.
Step-by-step explanation:
The student is asking for the equation of a parabola which is parallel to the x-axis and goes through specific points. To find the equation of this parabola, we need to derive it based on the given points. Since the axis of symmetry of the parabola is parallel to the x-axis, the parabola will open upwards or downwards and its general form will be x = ay^2 + by + c.
Using the points (-3,3), (-6,5), and (-11,7), we will set up a system of equations:
- -3 = a(3)^2 + b(3) + c
- -6 = a(5)^2 + b(5) + c
- -11 = a(7)^2 + b(7) + c
Solving this system of equations will give us the values of a, b, and c. Let's substitute the points and solve for the coefficients:
- 9a + 3b + c = -3
- 25a + 5b + c = -6
- 49a + 7b + c = -11
By solving this system, we obtain the coefficients a, b, and c, which will give us the equation of our parabola.