Calculate Point C on the Quadratic Graph of f(x)=x²-6x

The following function has been graphed below:

$f(x)=x^2-6x$

Calculate point C.

To solve this problem, we'll calculate the vertex of the parabola given by the quadratic function $f(x) = x^2 - 6x$.

• Step 1: Identify the coefficients $a = 1$ and $b = -6$.
• Step 2: Use the vertex formula $x = -\frac{b}{2a}$ to find the x-coordinate of the vertex.
• Step 3: Substitute the calculated x-coordinate back into the function to find the y-coordinate.

Now, let's compute:

Step 1: The function is $f(x) = x^2 - 6x$ with coefficients $a = 1$ and $b = -6$.

Step 2: Apply the vertex formula: $x = -\frac{-6}{2 \times 1} = \frac{6}{2} = 3$.

Step 3: For $x = 3$, substitute into $f(x)$ to find the y-coordinate:

$f(3) = (3)^2 - 6 \times 3 = 9 - 18 = -9$.

Therefore, the coordinates of the point C, which is the vertex, are $(3, -9)$.

The correct answer is $(3, -9)$, which corresponds to the given correct choice.