Question

For the graph of the function, f (x)=-3x^2 + 2x + 7.What is the x-coordinate of the turning point?

Answer 1

To find the x-coordinate of the turning point (vertex) of the quadratic function \( f(x) = -3x^2 + 2x + 7 \), we can use the formula for the x-coordinate of the vertex of a parabola given by the function in the standard form \( f(x) = ax^2 + bx + c \):

\[
x = -\frac{b}{2a}
\]

In your function, the coefficients are:
- \( a = -3 \)
- \( b = 2 \)

Now, substituting these values into the formula:

\[
x = -\frac{2}{2 \times -3} = -\frac{2}{-6} = \frac{1}{3}
\]

Thus, the x-coordinate of the turning point is \( \frac{1}{3} \).