Quadratic Function. Brainstorm Stylin’ Both are quadratics (parabolas) Not one-to-one (not...
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Transcript of Quadratic Function. Brainstorm Stylin’ Both are quadratics (parabolas) Not one-to-one (not...
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Quadratic Function
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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
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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
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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.
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y = x2
a = 1, b = 0, c = 0
Minimum point (0,0)
Axis of symmetry x=0
y=x2
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What happen if we change the value of a and c ?
y=3x2
y=-3x2
y=4x2+3
y=-4x2-2
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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.
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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.
![Page 10: Quadratic Function. Brainstorm Stylin’ Both are quadratics (parabolas) Not one-to-one (not invertible) Parent function is x^2 Both are positive Both.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649f3d5503460f94c5c8b7/html5/thumbnails/10.jpg)
Let’s investigate MAX and MIN
y=x2-4 y=x2+2x-15
y=-x2+5 y=-x2-1
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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
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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!
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? Explore
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=154
Describe the changes in your own words.
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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
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What are x intercepts also called?
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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)
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Find the Solutions
y=x2-4 y=x2+2x-15
y=-x2+5 y=-x2-1
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Find the solutions
y=x2+2x+1
y=-x2+4x-1
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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
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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
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Another Method to find ROOTS?
By factoring…let’s get it started
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Other Methods
By factoring…let’s get it started
By using the quadratic formula
2 4
2
b b acx
a
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The End