Last week, we talked about linear functions and lines and started with quadratic functions on Thursday. This week, we will finish with quadratic functions and start talking about exponential and log functions.
Linear functions represent lines on the plane, and are determined by two pieces of information: slope and an intercept, two points, slope and a point, etc. Any two points on the line can give you the slope (sometimes undefined as the line is vertical!). If the slope is positive, the linear function increases as x increases; if the slope is negative, the function decreases as x increases; if the slope is zero, the function does not increase or decrease. Setting y=0 give the x-intercept and setting x=0 gives the y-intercept. These are all information that helps you plot the graph of the line.
Quadratic functions are of the shape y=ax^2+bx+c, and setting y=0 gives the x-intercept(s) if any exists! We have seen last week, that the quadratic equation ax^2+bx+c=0 can have two distinct solutions, one solution or no solution. These three situations correspond to two x-intercepts, one x-intercept or no x-intercept in the graphs of our parabolas. In the process of looking for x-intercepts, we learned three methods: factoring, quadratic formula or completing the square. This coming Tuesday, we will keep using completing the square, as it gives more information: vertex. Vertex gives information on the maximum or minimum of the function and where the max/min is attained. We will also see some applications of quadratic functions in modeling.
Alright, that is it for now. Sorry for the late sum up, let me know if you have any questions!