Question

in the video, the instructor solved the quadratic equation x² + 4x = -4. the root of this quadratic equation is x = -2. what does this tell you about the graph of the parabola described by x² + 4x = -4?

Explanation:

A quadratic equation represents a parabola. When a quadratic equation has a single root (in this case $x = - 2$), it means the parabola touches the x - axis at exactly one point. This point is the vertex of the parabola and also the x - intercept.

Answer:

The parabola described by $x^{2}+4x=-4$ touches the x - axis at $x = - 2$, and $x=-2$ is both the x - intercept and the x - coordinate of the vertex of the parabola.