Question 1

IlusComplete the squareto find the vertexof this parabola.2.yº+4 x - 2y +21=0+([?], []).Enter

Question 2

Answer

The vertex of the parabola is (-5, 1)

Given the following equation:

y^2 + 4x - 2y + 21 = 0

Step-by-step explanation:

$\begin{gathered} y^2\text{ + 4x - 2y + 21 = 0} \\ \text{Step 1:} \\ \text{Isolate 4x} \\ 4x=-21+2y-y^2 \\ \operatorname{Re}-\text{arranging the equation} \\ -y^2\text{ + 2y - 21 = 4x} \\ -y^2\text{ +2y - 21 = 4x} \\ -y^2\text{ - }(2)/(2)y\text{ -21 = 4x} \\ -(y-1)^2\text{ -21 + 1 = 4x} \\ -(y^{}-1)^2\text{ - 20 = 4x} \\ \text{Divide all through by 4} \\ x\text{ = -}(1)/(4)(y-1)^2\text{ - 5} \\ U\sin g\text{ the equation} \\ x\text{ = }a(y\text{ }-k)^2\text{ + h} \\ \text{a = -}(1)/(4) \\ \text{h = -5} \\ \text{k = 1} \end{gathered}$

Vertex is (h, k)

Therefore, the vertex is (-5, 1)

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