X intercepts, Y intercepts, and Vertices

The X intercept is the point where the graph crosses the X axis, meaning the value of Y is 0.

The Y intercept is the point where the graph crosses the Y axis, meaning the value of X is 0.

Set the equation equal to 0: $$0 = (x - 3)^2 - 2$$ and solve for x.

The vertex is the highest or lowest point of the parabola, depending on its orientation.

A standard quadratic function has exactly one vertex.

A minimum vertex indicates that the parabola opens upwards.

A maximum vertex indicates that the parabola opens downwards.

By examining the coefficient of the squared term in the quadratic equation; if it's positive, the vertex is a minimum; if negative, it's a maximum.

The vertex helps determine the direction of the parabola and the range of the function.

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ .