Question
What are the coordinates of the vertex of y=-x^2+2x+1?
Answers
GPT 3.5
To find the coordinates of the vertex of a quadratic function in the form y = ax^2 + bx + c, you can use the formula x = -b/2a to find the x-coordinate of the vertex.
In this case, y = -x^2 + 2x + 1, so a = -1, b = 2, and c = 1.
x = -b/2a
x = -2/(2*(-1))
x = -2/-2
x = 1
To find the y-coordinate of the vertex, substitute the x-coordinate into the equation:
y = -1(1)^2 + 2(1) + 1
y = -1 + 2 + 1
y = 2
Therefore, the coordinates of the vertex are (1, 2).
In this case, y = -x^2 + 2x + 1, so a = -1, b = 2, and c = 1.
x = -b/2a
x = -2/(2*(-1))
x = -2/-2
x = 1
To find the y-coordinate of the vertex, substitute the x-coordinate into the equation:
y = -1(1)^2 + 2(1) + 1
y = -1 + 2 + 1
y = 2
Therefore, the coordinates of the vertex are (1, 2).