### Home > PC > Chapter 11 > Lesson 11.1.1 > Problem11-13

11-13.

Given the function $y = x^{2} − 4x + 13$:

1. Rewrite the function in the form $y = a\left(x − h\right)^{2} + k$ by completing the square. State the vertex of the parabola.

$y-13\:+\:?=x^2-4\textit{x}\:+\:?$ so that $y-k=(x-h)^2$

2. Using the equation you found in part (a) or the Quadratic Formula, find the roots of the function.

The roots are the $x$-intercepts. Let $y = 0$ to find the $x$-intercepts.

3. What must be true about the graph of the parabola if the roots are non-real numbers?

It has no $x$-intercepts.