Today we covered section 9.3 and 9.4, about graphing a quadratic function and how to solve a quadratic equation with graphing.<\/p>\n
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.<\/p>\n
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.<\/p>\n
Students are still uncomfortable working with letters like a, b, c (representing constands)\u00a0in 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.<\/p>\n
To graph a quadratic function y = ax^2 + bx +c, follow the following steps:<\/p>\n
1. Find the vertex with the formulae, find its y value;<\/p>\n
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.<\/p>\n
3. Connect those points with a smooth curve.<\/p>\n
The solution to a quadratic equations, also called roots, are x-intercepts on the graph. So to solve a quadratic equation with graphing:<\/p>\n
1. rewrite the equation into the form of ax^2 + bx +c = 0<\/p>\n
2. Graph the quadratic function y = ax^2 + bx + c<\/p>\n
3. Find the x-intercepts. These are your solutions.<\/p>\n
4. Check the answer algebratically.<\/p>\n
Below is the link to the homework for today:<\/p>\n