TAKS Blitz Competition Quadratic Functions. The Parabola

TAKS Blitz Competition

Quadratic Functions

The Parabola

The Axis of Symmetry

The Vertex

The vertex is always either the minimum value or the maximum value.

The Parent Function

2y x

The Parameters

The parameters of a quadratic are a, b, and c.

In the example below a=2, b=3 and c=5.

2y ax bx c

22 3 5y x x

Transforming a Quadratic

Changing the negation of the ‘a’ parameter flips the parabola.

2y x

2y x

Transforming a Quadratic

Changing the value of the ‘a’ parameter changes how thin or wide the parabola is.

2y x22y x23y x24y x

Transforming a Quadratic

Changing the value of the ‘c’ parameter changes where the vertex is.

Transforming a Quadratic

What about the value of the ‘b’ parameter of the quadratic. When the ‘b’ value changes all sorts of cool things happen, but that’s beyond the scope of this class. Can’t wait till next year to find out what? Then go exploring with your calculator.

Solving a Quadratic

A Quadratic Function can have two “answers.”

The “answers” to a quadratic can be called any of these things:

The ZerosThe RootsThe SolutionsThe x-intercepts

The Solutions

Methods to Solve

You can find the solution to a Quadratic several ways including:

Quadratic FormulaUsing the table in the calculatorFactoringGuess and Check

We’re going to go over two of these methods.

Solving a Quadratic

Find the solutions: 4=x2+3x

Move everything to one side: 0=x2+3x-4

Enter into the calculator as: y1=x2+3x-4

Look at the table:

The solutions are: (-4,0) and (1,0)

The roots are: -4 and 1

X Y

-4 0

1 0

Checking the solutions

Equation: 4=x2+3x

Solutions: (-4,0) and (1,0)

Check (-4,0)

4=x2+3x

4=(-4)2+3(-4)

Check (1,0)

4=x2+3x

4=(1)2+3(1)

The End

You now know the basics of understanding Quadratics. Remember, this is just the beginning. You’ll learn a lot more about Quadratics in Algebra II or Math Models next year.

Continue to the next slide if you’re ready to take a quick quiz!!

QUIZ TIME

Okay, it’s time to see what you learned.

Get your thinking caps on....

Ready, set, go.....

Quadratic Quiz Question 1

Quadratic Quiz Question 2

Quadratic Quiz Question 3

Quadratic Quiz Question 4

Quadratic Quiz Question 5