## Graphing Linear and Quadratic Functions

#### Aligned To Common Core Standard:

**High School Interpreting Functions** - HSF-IF.C.7a

How to Graph Linear and Quadratic Functions - When the students are introduced to graphing equations, they usually start with linear and quadratic equations.
Linear equations are the ones where the highest power of the variable is 1, and quadratic equations are the ones with the highest power 2.
**Graphing Linear Equations** - When graphing linear equations, you have to start by finding the x-intercepts and y-intercepts. The x-intercept is where the straight line cuts the x-axis, and here y-value is zero. The y-intercept is where the line cuts the y-axis and here, the value of x is zero.
You can mark these two points on the graph and use a ruler to join these points to create a line.
**Graphing Quadratic Equations** - Similar to linear graphing equations, when you are graphing quadratic equations, you have to find the x- and y-intercepts. You can place zero in place of x in the equation to find the y-intercept and place zero in place of y in the equation for the y-intercept.
As quadratic equations represent a curve, you will have to find out the vertex of the curve. It is the point where the value of y is maximum or minimum.
To calculate the x-value of the vertex, you can use the formula; x=(-b)/2a
Here, b = coefficient of x, a = coefficient of x^{2}
After you find the x-value, you can then substitute it into the equation and find the corresponding value of y.
You can then sketch a line of symmetry from this point, and it will help you graph the curve accurately. To give your curve a more definite shape, you can use a set of x-values and determine their corresponding y-values and use the table to plot the graph.

### Printable Worksheets And Lessons

- Graph a Linear Function
Step-by-step Lesson- We start out pretty simple. They should
have this skill from previous studies.

- Guided Lesson
- I usually get a blank stare from kids when they see number two
for the first time. After they do one, its a cinch for them.

- Guided Lesson Explanation
- I did drag out the thoughts required here, just a little.

- Practice Worksheet
- The kids should whip right through this, assuming they did the
guided lesson.

- Matching Worksheet - See how the graph matches work out for you.

#### Homework Sheets

The graphs have a blue background to help the contrast come across when printing.

- Homework 1 - The x-intercept is the x-coordinate of the point where the graph crosses the x-axis. The coordinates of the x-intercept are (x, 0), where x is the x intercept.
- Homework 2 - The y-intercept is the y-coordinate of the point where the graph crosses the y-axis. The coordinates of the y-intercept are (0, y), where y is the y intercept.
- Homework 3 - Graph this function using intercepts: 24x + 7y = 48

#### Practice Worksheets

Using just the intercepts can be very powerful when answering multiple choice questions.

- Practice 1 - Pay attention to the y-intercept it drives everything.
- Practice 2 - Y = 8/4 x
- Practice 3 - Graph this line using the slope and y-intercept: Y = 32/8 x

#### Math Skill Quizzes

The answer keys are just rough sketches. You are just looking for the trends here.