Question

What is the standard form of the equation of a parabola that has a vertex of (-1,10) and passes through the point (2,-8)?

A) y = 2(x + 1)² + 10
B) y = 2(x - 1)² + 10
C) y = -2(x + 1)² + 10
D) y = -2(x - 1)² + 10

Answer 1

The standard form of a parabola with a vertex at (-1,10) and passing through (2,-8) is y = -6(x + 1)² + 10, which doesn't match any of the provided options.

Step-by-step explanation:

The standard form of a parabola's equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Given the vertex (-1,10) and that the parabola passes through the point (2,-8), we can substitute these values into the equation to find the coefficient a.

Using the vertex, the equation becomes y = a(x + 1)² + 10. Substituting the point (2, -8) into this equation yields -8 = a(2 + 1)² + 10. Solving for a gives us a = -6. The correct standard form equation of the parabola is then y = -6(x + 1)² + 10, which is not one of the options provided, meaning there may be an error in the question or options.