Write the equation for a parabola that has a vertex (2, -1) and a directrix of x = 5.

The equation of the parabola that has a vertex (2 , -1) and a directrixof x = 5 is (y + 1)² = -12(x - 2)Step-by-step explanation:Let us revise the equation of a parabola1. The form of the equation is (y − k)² = 4p(x − h)2. The coordinates of its vertex are (h , k)3. The equation of its axis of symmetry is y = k4. The coordinates of the focus are (h + p , k)5. The directrix is at x = h − p∵ The coordinates of the vertex of the parabola are (2 , -1)∵ The coordinates of its vertex are (h , k)∴ h = 2 and k = -1∵ The directrix is at x = 5∵ The directrix is at x = h − p∴ h - p = 5∵ h = 2∴ 2 - p = 5- Subtract 2 from both sides∴ - p = 3- Multiply both sides by -1∴ p = -3∵ The form of the equation is (y − k)² = 4p(x − h)∴ (y - -1)² = 4(-3)(x - 2)∴ (y + 1)² = -12(x - 2)The equation of the parabola that has a vertex (2 , -1) and a directrixof x = 5 is (y + 1)² = -12(x - 2)Learn more:You can learn more about equation of a parabola in brainly.com/question/8054589#Learnwithbrainly