Given the information below, write the equation in Standard Form.

Parabola:

Vertex (3, - 2)

Focus (5, - 2)

The standard form of the equation of the parabola is (y + 2) ² = 8 (x - 3)

Step-by-step explanation:

The standard form of the equation of a parabola is (y - k) ² = 4p (x - h), where

The vertex of the parabola is (h, k) The focus is (h + p, k)

∵ The vertex of the parabola is (3, - 2)

∴ h = 3 and k = - 2

∵ The focus is (5, - 2)

∴ h + p = 5

- Substitute h by 3 to find p

∵ 3 + p = 5

- Subtract 3 from both sides

∴ p = 2

∵ The standard form of the equation of the parabola is (y - k) ² = 4p (x - h)

- Substitute the values of h, k, and p in the equation

∴ (y - - 2) ² = 4 (2) (x - 3)

∴ (y + 2) ² = 8 (x - 3)

The standard form of the equation of the parabola is (y + 2) ² = 8 (x - 3)