Answer
The vertex of the parabola is (-5, 1)
Given the following equation:
y^2 + 4x - 2y + 21 = 0
Explanation:
[tex]\begin{gathered} y^2\text{ + 4x - 2y + 21 = 0} \\ \text{Step 1:} \\ \text{Isolate 4x} \\ 4x=-21+2y-y^2 \\ \operatorname{Re}-\text{arranging the equation} \\ -y^2\text{ + 2y - 21 = 4x} \\ -y^2\text{ +2y - 21 = 4x} \\ -y^2\text{ - }\frac{2}{2}y\text{ -21 = 4x} \\ -(y-1)^2\text{ -21 + 1 = 4x} \\ -(y^{}-1)^2\text{ - 20 = 4x} \\ \text{Divide all through by 4} \\ x\text{ = -}\frac{1}{4}(y-1)^2\text{ - 5} \\ U\sin g\text{ the equation} \\ x\text{ = }a(y\text{ }-k)^2\text{ + h} \\ \text{a = -}\frac{1}{4} \\ \text{h = -5} \\ \text{k = 1} \end{gathered}[/tex]Vertex is (h, k)
Therefore, the vertex is (-5, 1)
