Quadratic Function

Brainstorm Stylin’ Both are quadratics (parabolas) Not one-to-one (not invertible) Parent function is x^2 Both are positive Both are continuous One goes through the origin Polynomial Both go through at least two quadrants Passes vertical line test and fails the

horizontal line test

Advanced Algebra 2 – Unit 210/20/2011 AGENDADO NOW: Quadratic or

NO?Look to the right of the

boardAgenda: Portfolio Recap

More Quadratic VOCABThink Pair Share

FOILING Quadratics

We will: Analyze the value and

consequence of “a” coefficients

Determine the role does “b” play

Determine the vertex – MAX/MIN

Calculate SOLUTIONS, roots, intercepts & zeros

Quadratic Function(y = ax2 + bx + c) a, b, and c are called

the coefficients. The graph will form

a parabola. Each graph will have

either a maximum or minimum point.

There is a line of symmetry which will divide the graph into two halves.

y = x2

a = 1, b = 0, c = 0

Minimum point (0,0)

Axis of symmetry x=0

y=x2

What happen if we change the value of a and c ?

y=3x2

y=-3x2

y=4x2+3

y=-4x2-2

Recap(y = ax2+bx+c)

When a is positive,

When a is negative,

When c is positive When c is negative

the graph concaves UPWARD. happy

the graph concaves downward. sad.

the graph moves up c units.

the graph moves down c units.

Quadratic Function(y = ax2 + bx + c) a, b, and c are called

the coefficients. The graph will form

a parabola. Each graph will have

either a maximum or minimum point.

There is a line of symmetry which will divide the graph into two halves.

Let’s investigate MAX and MIN

y=x2-4 y=x2+2x-15

y=-x2+5 y=-x2-1

What do you notice about max/min and line of symmetry? Think pair share (2min)

y=x2-4 y=x2+2x-15

y=-x2+5 y=-x2-1

VERTEX: –b/2a, f(-b/2a)

y=x2-4

y=x2+2x-15

y=-x2+2x -15

y=-2x2-x +4

Work with a friend – be ready to present!

? Explore

http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=154

Describe the changes in your own words.

Solving Quadratic Functions(ax2 + bx + c = 0)

Since y = ax2 + bx +c , by setting y=0 we set up a quadratic equation.

To find the solutions means we need to find the x-intercept(s).

X-intercepts are also called ROOTS To make your life more complicated,

they are also called ZEROS

What are x intercepts also called?

Solving Quadratic Functions(ax2 + bx + c = 0)

We know what a parabola looks like, so how many solutions or roots or zeros or x-intercepts can there be??

Think Pair and share out (3 minutes)

Find the Solutions

y=x2-4 y=x2+2x-15

y=-x2+5 y=-x2-1

Find the solutions

y=x2+2x+1

y=-x2+4x-1

Observations

Sometimes there are two solutions. Sometimes there is only one solution.

Sometimes there is no solution at all…well…there are imaginary solutions…you are going to love them

To solve quadratic equations(graphing method) X2 - 2x = 0 We could put y = x2-x into a

calculator or sketch it to find x intercepts.

This one has two solutions, x=0 and x=2.

y=x2-2x

Another Method to find ROOTS?

By factoring…let’s get it started

Other Methods

By factoring…let’s get it started

By using the quadratic formula

2 4

2

b b acx

a

The End