Find the coordinates of the turning point on the graph of y=3x 2 −2x−1

The turning point of a quadratic function y = ax^2 + bx + c is given by the formula (-b/2a, f(-b/2a)).

Here, a = 3, b = -2, and c = -1.

Step 1: Find the x-coordinate of the turning point The x-coordinate of the turning point is given by -b/2a. Substituting the given values, we get:

x = -(-2) / (2*3) = 2/6 = 1/3

Step 2: Find the y-coordinate of the turning point The y-coordinate of the turning point is the value of the function at x = 1/3. Substituting x = 1/3 into the equation, we get:

y = 3*(1/3)^2 - 2*(1/3) - 1 = 3/9 - 2/3 - 1 = 1/3 - 2/3 - 1 = -1/3 - 1 = -4/3

So, the turning point of the graph y = 3x^2 - 2x - 1 is (1/3, -4/3).