Find Point C on f(x)=x²-8x+16: Quadratic Function Graph Analysis

Looking at the graph, point C is clearly marked on the horizontal line where y = 0. Any point on the x-axis has a y-coordinate of 0.

The function $f(x) = x^2 - 8x + 16$ is a perfect square trinomial: $(x-4)^2$. This means the parabola just touches the x-axis at x = 4, creating a double root.

You can always use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$. For this problem: $x = \frac{8 \pm \sqrt{64-64}}{2} = 4$

Since point C is at x = 4 on the x-axis, the y-coordinate is 0. Write it as an ordered pair: (4, 0) where x comes first, then y.

No! A quadratic function can have at most 2 x-intercepts. This perfect square has exactly one x-intercept at x = 4, making point C unique.