Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2...

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Anatomy of a Quadratic Function

Transcript of Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2...

Page 1: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Anatomy of a Quadratic Function

Page 2: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Quadratic Form

Any function that can be written in the form Ax2+Bx+C where a is not equal to zero.

You have already been looking at quadratics

Anything with an x2 term in the equation

Page 3: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Creating a quadratic

Done by foiling Example (3x+2)(2x-4)

Page 4: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

To be a quadratic…

Must have an x2 term Must have a constant number not

equal to zero. Proper form: Ax2+ Bx +C Practice identifying

Page 5: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Create the quadratic…

Foil to get the quadratic, and label a, b, and c

(2x-1)(3x+5)

Page 6: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Foil to get the quadratic, and label a, b, and c

(2x-5)(x-2)

Page 7: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Quadratic Function

How do I know it’s a function?

Page 8: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

The parabola Graph of a quadratic function is a parabola It’s the “U” shape Upward opening parabola- the coefficient

with the x2 term is positive

Page 9: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Downward opening parabola- The coefficient with the x2 term is negative

Page 10: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Axis of Symmetry

Each parabola has an axis of symmetry

Axis of symmetry- line that divides a parabola into two parts that are mirror images of one another

DO IT

Page 11: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

The parabola

Vertex- lowest point or highest point on a graph

Page 12: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Max and Min Values

If the parabola opens up, the min value is at the vertex

If the parabola opens down, the max value is at the vertex

Page 13: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

The axis of symmetry passes through the vertex of the parabola

Page 14: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Domain and Range

Domain of a parabola is all real numbers

Page 15: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Range of a parabola

Depends on where the parabola sits…

Page 16: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Solving Quadratic Functions

Page 17: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Square Roots

x2=a where a is any number greater than or equal to 0

x is called the square root of a The solution, x has two values

aa ,

Page 18: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Properties of Square Roots

Positive square root is called the principal root

Properties of square roots

b

a

b

aba

baabba

,0,0

*,0,0

Page 19: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Solve

Solve just like a regular equation Follow order of operations, but leave

square root till the end Simplify all other ways first

Page 20: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

4x2 +13=253

Page 21: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

5x2-19=231

Page 22: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

9(x-2)2=121

Page 23: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

4(x+2)2=49

Page 24: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Warm Up!

Complete this problem at the bottom of your sheet

Solve 4x2+5=20

Page 25: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Solving using the Calculator

Quadratic formulas can have more than one solution

Because a square root of a number can give a positive and negative number

They can also have no solutions, or just one

Page 26: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

So how do I know if I am right?

Use your calculator Solve so the entire equation is set

equal to 0 Go to y= on your calculator Plug the equation into y1 Look for the x intercepts of the graph Use the Solve key to find values

Page 27: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Pythagorean Theorem

a2 + b2 =c2

Works only for right triangles What is a right triangle?

Page 28: Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Homework: page286

#15, 18, 21, 24, 27, 30


addmath form 4 Chapter 2 - Quadratic Function

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