taks blitz competition quadratic functions. the parabola
TRANSCRIPT
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TAKS Blitz Competition
Quadratic Functions
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The Parabola
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The Axis of Symmetry
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The Vertex
The vertex is always either the minimum value or the maximum value.
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The Parent Function
2y x
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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
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Transforming a Quadratic
Changing the negation of the ‘a’ parameter flips the parabola.
2y x
2y x
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Transforming a Quadratic
Changing the value of the ‘a’ parameter changes how thin or wide the parabola is.
2y x22y x23y x24y x
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Transforming a Quadratic
Changing the value of the ‘c’ parameter changes where the vertex is.
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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.
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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
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The Solutions
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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.
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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
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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)
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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!!
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QUIZ TIME
Okay, it’s time to see what you learned.
Get your thinking caps on....
Ready, set, go.....
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Quadratic Quiz Question 1
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Quadratic Quiz Question 2
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Quadratic Quiz Question 3
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Quadratic Quiz Question 4
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Quadratic Quiz Question 5