# Week 8 – Precalc 11

For the eighth week of Precalc 11, we started our new unit — Analyzing Quadratic Functions and inequalities.

Key Learning：

Every quadratic function can be written in the form y = ax^2+bx+c, where a, b, and c are real numbers and a is not zero.

First, we learned the properties of quadratic functions and how to analyze the quadratic equation. We learned that when are given the quadratic equation in vertex form then we can graph the equation.

Second, we learned the quadratic equation $ax^2 + bx + c = 0$, this unit we learned $y = a(x-p)^2 + q$. This is combination of the equations $y = (x-p)^2, y = x^2$, and $y = x^2 + q$. These equations are all very important in graphing the curve the equations make.

Example：

Graph y = (x− 2)^2− 4

• Vertex = (2,4)
• x-intercept: 0 and 4
• y-intercept: 0
• opens up (happy)