Find the vertex of the function. Write your answer in the form (x,y). Use the slash mark as a fraction bar if necessary.
y=x^2-x-23
0=2x-1
x=1/2, y=1/4-1/2-23=-23.75
That is with Calculus. Now in Algebra, do this
y=x^2-x + xxxx -23-xxxxx
we are going to make a difference of prefect squares.
y=x^2-x+1/4 -23-1/4
y= (x-1/2)^2 - (sqrt22.75)^2
so clearly, this is a minumum at x=1/2
To find the vertex of a quadratic function in the form y = ax^2 + bx + c, you can use the formula x = -b/2a.
In your case, the quadratic function is y = x^2 - x - 23.
Comparing it to the standard form y = ax^2 + bx + c, we have a = 1, b = -1, and c = -23.
Now, we can substitute these values into the formula x = -b/2a:
x = -(-1) / 2(1)
x = 1 / 2
x = 1/2
To find the y-coordinate of the vertex, we substitute this value of x back into the original equation:
y = (1/2)^2 - (1/2) - 23
y = 1/4 - 1/2 - 23
y = -110/4
y = -55/2
Therefore, the vertex of the function y = x^2 - x - 23 is (1/2, -55/2).