Answer:
The equation is (y + 1)² = 4(x - 4)
Explanation:
The equation of the graph of the quadratic equation (Parabola) in standard form is (y - k)² = 4p(x - h), where
- The vertex of the parabola is (h, k)
- The directrix is at x = h - p
∵ The vertex is (4, -1)
∴ h = 4 and k = -1
∵ The directrix is at x = 3
∵ The directrix is at x = h - p
∴ h - p = 3
→ Substitute the value of h to find the value of p
∵ 4 - p = 3
→ Subtract 4 from both sides
∴ 4 - 4 - p = 3 - 4
∴ - p = -1
→ Divide both sides by -1
∴ p = 1
→ Substitute the values of h, k, and p in the form of the equation above
∵ (y - -1)² = 4(1)(x - 4)
∴ (y + 1)² = 4(x - 4)
∴ The equation is (y + 1)² = 4(x - 4)