Chapter 9.1, Problem 6CYU

To determine

To find the vertex, the equation of the axis of symmetry, the y-intercept and the zeroes pf each graph.

Answer to Problem 6CYU

The vertex is at $\left(0,-1\right)$ , equation of axis of symmetry is $x=0$ , y-intercept is at $\left(0,-1\right)$ and the zeroes are at $\left(-1,0\right)$ and $\left(1,0\right)$ .

Explanation of Solution

Given information :

The graph is provided from which the required solutions are to be derived.

1. Determine the vertex. Since the parabola opens upwards, there is a minimum point and the vertex is located at $\left(0,-1\right)$ .
2. To compute the axis of symmetry, find the line that bisects the parabola into two equal halves. It is a cross-section. In this case, the equation of the axis symmetry is at $x=0$ .
3. The point at which the parabola intersects the y-axis, this the point of the y-intercept. This point has a zero figure for the x-coordinate. For this figure, the y-intercept is at the point $\left(0,-1\right)$ .
4. The points wherein the parabola intersects the x-axis, are the zeros. There could be at most two zeros for each parabola. This figure has zeroes at $\left(-1,0\right)$ and $\left(1,0\right)$ .