Question

Suppose a parabola has a vertex (-4, 7) and also passes through the point (-3, 8). What is the equation of the parabola in vertex form?

Answer 1

The equation of the parabola with a vertex at (-4, 7) and passing through the point (-3, 8) is y = (x + 4)^2 + 7.

Step-by-step explanation:

To find the equation of the parabola in vertex form given the vertex (-4, 7) and a point (-3, 8) through which it passes, we can use the following steps:

• Write the equation of a parabola in vertex form: y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
• Substitute the vertex into the equation: y = a(x + 4)^2 + 7.
• Plug the point (-3, 8) into the equation and solve for 'a': 8 = a(-3 + 4)^2 + 7.
• Simplify and solve for 'a': 1 = a(1)^2, which gives us a = 1.

With 'a' found, we can write the final equation of the parabola: y = (x + 4)^2 + 7.