This packet helps students understand how to graph quadratic equations by finding the x-intercepts first. There are many ways to graph quadratic equations (which graph as parabolas). One way is to find the x-intercepts (where the parabola crosses the x-axis), which are also called the roots or solutions of the quadratic equations. Once students find the x-intercepts, they can find the vertex of the graph (students can find the x coordinate of the vertex using the formula $\dfrac{-b}{2a}$ and then plug that into the equation to find the y value of the vertex, or (as shown in the video below) they can find the average of the x values of the x-intercepts and then plug in for y), and the rest of the graph should be fairly easy to fill in.

Each page starts with easier problems that get more difficult as students work through the packet. Easier problems start with quadratic equations that have already been factored. More advanced problems require students to factor the quadratic equation in order to find the x-intercepts.

The first 12 problems just ask students to find the x-intercepts of each equation. The last 8 problems also provide students with a coordinate plane a blank table of values so that they can figure out and plot the entire parabola.

After doing all 20 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them.

*Sketch the graph of the function using the x-intercepts.*

Simple:

$y= (x-1)(x+1)$

Advanced:

$y= x²-x-12$

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

Students should also be familiar with factoring polynomials (see all practice work for factoring polynomials here) and especially with factoring quadratic equations ($ax^2+bx+c$).