This week, we continued with our unit on “Analyzing Quadratic Functions.” It’s not the easiest unit, but it is very similar to our previous unit so I think that’s the main reason I understand a big portion of it.
I want to talk about the main thing that we worked on this week; the standard form equation: y = a(x – p)² + q, this is the equation that we have been using this week to help us form parabolas on our graphs (the equation gives us hints as to where we should start).
In this equation: y = a(x – p)² + q, the a”” value tells us how skinny/narrow/wide the parabola is and whether it opens upwards or downwards. If “a” is equal to 1, the parabola will have a 1x3x5 pattern, if “a” is less than 1, the parabola gets skinnier, if “a” is in between 0 and 1, the graph gets wider and lastly, is “a” is less than 1, the parabola will open downwards. The “p” value in the equation lets you know whether the parabola slides left or right, another term for this is “Horizontal Equation,” it also gives you a clue about the line of symmetry. The “q” in the equation lets you know whether the parabola slides up or down – the “Vertical Translation.” Also (P,Q) gives you the vertex, which helps you start your question.
Here is an example on how we analyze this quadratic function: