# From Linear to Quadratic Worksheets

Linear equations create a straight line when they are graphed, hence the name linear. This means that the first differences are always the same. These types of equations follow the form of Ax + By + C = 0. They do not involve any power higher than one for all the variables. Quadratic equations form sweet curves when they are graphed. They are equations in which one or more of terms is squared but raided to no higher power. Which means they lend themselves to being used to calculate trajectories. Quadratic equations follow the form: Ax^{2} + By + C = D. On the worksheets and lessons that we work with on this page you will learn how to graph both these forms of equations. We will then begin to learn how to evaluate the nature of these graphs.

### Aligned Standard: HSF-IF.C.7a

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

- Quiz 1 - Where is the x output for you on this?
- Quiz 2 - Why would you want to more than just an output?
- Quiz 3 - These graphs are neat to see.

### 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. Linear equations follow the format: y = mx + b. x and y are just the ordered pair that is located on the line. m indicates the slope of line (rise over run). The b variable indicates where the crosses the y axis (y-intercept.) If you simply pick a value for either x or y and run it through the equation, you can determine the complimentary ordered pair location.

**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.