Question

How do you graph and label the vertex and axis of symmetry of `y=-0.25(x+1.5)^2-1.25`?

Answer 1

We are given: vertex, direction of opening, and the factor of transformation - enough information to allows us to graph.

Axis of symmtery is the `x`-value of the vertex.

Explanation:

In terms of graphing, given the equation in vertex form, makes graphing exponentially easier.

This is because we are given multiple things that allows us to graph immediately without doing additional calculations.

We are given:

1. The vertex. It is the `h`- and `k`-values. Therefore, our vertex is `(-1.5, -1.25)`. The axis of symmetry is simply the `x`-value of the vertex. Therefore, the axis of symmtery is `x=-1.5`. Remember, it's an equation.
2. Direction of opening. If the `a`-value is positive, the parabola opens up, giving us a minimum value. If it is negative, it opens down, giving us a maximum value. That is the case in this equation.
3. The factor of vertical compression/stretch. The `a`-value itself is less than `1`, meaning the parabola is vertically compressed.

With all this information, we can graph. As a result, we get this:

graph{-0.25(x+1.5)^2 - 1.25 [-10, 10, -5, 5]}

Hope this helps :)