Sections 5.1-5.3. What is a “quadratic” function?

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Presentation transcript:

Sections

What is a “quadratic” function?

Graph of a quadratic function…

What must you be able to do with quadratic functions right now? 1) Graph a quadratic function (either in standard or vertex form) 2) Convert a quadratic function to either standard or vertex form given the other form 3) Write a quadratic function (in either form) given information

Procedure for graphing quadratic functions (in standard form)…

5) Select two other values of x and solve for their y- values; plot these points (if possible, choose 0 as one of your values!) 6) Find the “reflection (corresponding) points” of those two points and plot these points as well 7) Draw your graph through your points…done! No parab-lem!

Let’s graph some parabolas!

There is another form…

Procedure for graphing quadratic functions (in vertex form)… use same procedure as before (start at step #4)

Let’s graph some more parabolas!

Family Reunion!

Let’s try some…

Writing Quadratic Functions…

When given a table of values: - press STAT, then choose option 1 EDIT - enter the data (each row is a column on the calculator) - after you finished entering the data, press STAT, move the cursor to CALC, then choose option 5 QUADREG (Quadratic Regression Line) - write the quadratic function using the information given

Let’s try some… Given the following table of values, determine the quadratic function associated with them: A) B)

Translations… one can use vertex form to write “translation equations” of quadratic functions translation- when a graph is moved around the coordinate plane (does not affect either size of shape of graph) - three types of translations: horizontal, vertical, and diagonal translations start from “parent functions” (the function representing the graph that is to be moved)

Translations… Rules for writing translation equations: - if you move left, the sign inside the parentheses is positive - if you move right, the sign inside the parentheses is negative - if you move up, the sign at the end of the function is positive - if you move down, the sign at the end of the function is negative

Let’s try some…