Determine the vertex of the quadratic equation:
10) $y=-x^{2}+2 x+4$

Answer

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Answer

$\boxed{(1, 5)}$ is the final answer.

Steps

Step 1 ：The vertex of a quadratic equation in the form $y = ax^2 + bx + c$ is given by the point $-\frac{b}{2a}, f(-\frac{b}{2a})$.

Step 2 ：For the given equation $y = -x^2 + 2x + 4$, we have $a = -1$ and $b = 2$.

Step 3 ：So, the x-coordinate of the vertex is $-\frac{b}{2a} = -\frac{2}{2*(-1)} = 1$.

Step 4 ：Substitute $x = 1$ into the equation to find the y-coordinate of the vertex: $y = -(1)^2 + 2*1 + 4 = -1 + 2 + 4 = 5$.

Step 5 ：So, the vertex of the quadratic equation $y = -x^2 + 2x + 4$ is $(1, 5)$.

Step 6 ：$\boxed{(1, 5)}$ is the final answer.