Where is the vertex of the graph of
y = -x squared + 4x + 5
To find the vertex of a quadratic function in the form of y = ax^2 + bx + c, you can use the following formula:
x-coordinate of the vertex = -b / (2a)
In your case, the quadratic function is y = -x^2 + 4x + 5. By comparing it to the general form, we can see that a = -1, b = 4, and c = 5. Now we can substitute these values into the formula:
x-coordinate of the vertex = -4 / (2 * -1) = -4 / -2 = 2
To find the y-coordinate of the vertex, substitute the x-coordinate (2) back into the original equation:
y = -(2)^2 + 4(2) + 5
y = -4 + 8 + 5
y = 9
Therefore, the vertex of the graph is located at (2, 9).
x^2 - 4 x - 5 = -y
x^2 - 4 x = -y + 5
x^2 - 4 x + 4 = -y + 9
(x-2)^2 = -(y-9)
so
(2,9)