QuestionTicket: Identify the following the graph: vertex: $(4,-1)$ Focus: $(4,1)$ P -value: 5 Directrix: $y=-9$

Studdy Solution
Verify the equation with given values:
Check that the focus and directrix satisfy the equation:
- The focus $(4, 1)$ should satisfy $(x - 4)^2 = 8(y + 1)$:
$$(4 - 4)^2 = 8(1 + 1)$$ $$0 = 16$$
- The directrix $y = -9$ is consistent with the vertex form since $y = -9$ is below the vertex.
The equation of the parabola is:
$$\boxed{(x - 4)^2 = 8(y + 1)}$$