Today we covered section 9.3 and 9.4, about graphing a quadratic function and how to solve a quadratic equation with graphing.

We talked about the shape of a quadratic function, a parabola, how to use the value of a to determine whether the u-shaped parabola opens up (when a > 0) or opens down (when a < 0). We have the formulae to find the x value of the vertex: x = – b/2a. We talked about how to find the y value at the vertex. We talked about the axis of symmetry, which is the vertical line passing through the vertex.

As the shape of a parabola is a U-shape, when it opens up, there is a minimum value of the y at the vertex. Similarly, when it opens down, there is a maximum value of y at the vertex.

Students are still uncomfortable working with letters like a, b, c (representing constands) in place of specific numbers, as in y = ax^2 + bx + c. When I ask them with a specific number, they will give me an answer. But if I ask with something with a/b/c, they look at me, puzzled. This takes time, as they are still getting into algebra.

To graph a quadratic function y = ax^2 + bx +c, follow the following steps:

1. Find the vertex with the formulae, find its y value;

2. Make a table with the vertex in the middle, do one side (as the other side is symmetric), +1, +2, +3, find the corresponding y values.

3. Connect those points with a smooth curve.

The solution to a quadratic equations, also called roots, are x-intercepts on the graph. So to solve a quadratic equation with graphing:

1. rewrite the equation into the form of ax^2 + bx +c = 0

2. Graph the quadratic function y = ax^2 + bx + c

3. Find the x-intercepts. These are your solutions.

4. Check the answer algebratically.

Below is the link to the homework for today:

http://blog.newtonchineseschool.org/wangweidong/files/2011/12/Math7_Fall_HW_L10.pdf

Feel free to contact me for any question.