# Graphing Quadratic Equations: Finding the Vertex

This packet helps students understand how to graph quadratic equations starting with finding the vertex. There are many ways to graph quadratic equations (which graph as parabolas). Finding the vertex (the highest or lowest part of the parabola) is one of the first ways that students learn. They use the formula $\dfrac{-b}{2a}$ to find the x coordinate of the vertex (students can find the a and b values by putting the equation into standard form: $ax^2+bx+c=y$), plug that x value into the equation to find the y coordinate of the vertex, and then they know where to start graphing. An equation with a negative $x^2$ will open downward and an equation with a positive $x^2$ will open upward. Once they plot the vertex, students can enter in other x values to find a few more points and graph out the rest of the parabola (which will be symmetrical).

Problems include a quadratic equation, a coordinate plane for graphing, and an empty table of values that students can use to keep track of coordinates before they start plotting points.

Each page starts with easier problems that get more difficult as students work through the packet. After doing all 12 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them.

*Find the vertex of the graph, complete a table of values, and graph the function. *

Simple:

$y= x²+2x+1$

Advanced:

$y= 2x²+2x+1$

Practice problems require knowledge of graphing on a coordinate plane and addition, subtraction, multiplication, and division of integers.