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Section 2.1 Transformations of Quadratic Functions
Honors Algebra 2 Section 2.1 Transformations of Quadratic Functions
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Essential Question How do the constants a, h and k transform the parent quadratic function graph? π¦= π₯ π¦=π (π₯ββ) 2 +π
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The graph of a quadratic function is a parabola.
Do exploration 1 on page 47 with a partner
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Translations βhβ and βkβ move the parabola horizontally or vertically
The size and shape of the parabola does NOT change. Recall the jingle: Add to x, go _______ Add to y, go _______
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This quadratic function is
written in vertex form. It is very easy to figure out what the vertex is. Different values of βaβ do not change the vertex.
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Reflections If x is replaced with a negative x, the graph flips across the y axis. The graph looks exactly the same. If y (f(x)) is replaced with a negative y, the graph flips across the x axis. In other words, βaβ is negative. You have a sad face parabola.
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Stretches and shrinks βaβ changes the shape of the parabola
When a is greater than 1, you have a βskinnyβ parabola When the absolute value of a is between 0 and 1, you have a βchubbyβ parabola
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For the parent quadratic function, the vertex (turning point) is at (0,0)
When the function is transformed, the vertex may change. The new vertex is at (h,k).
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Writing a transformed quadratic function using the parent function
Write a transformation function that is translated 4 units left and 3 units down, followed by a reflection in the y axis. Do the translation 1st. Then flip the graph.
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Challenge You can also transform a function that is not the parent function! π π₯ =4 π₯ 2 β3 Write a new function g that is translated 1 unit to the right followed by a reflection in the y-axis.
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Standard form of a quadratic function
The standard form equation looks like this: π=π π π +ππ+π To make the change -square the binomial (remember FOIL?) -combine like terms
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Real life Think of some real life examples of parabolas!
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When an object is thrown or shot upward, gravity takes over and it follows a parabolic curve.
β π‘ =βπ π‘ 2 + π£ 0 π‘+ β π g=4.9 (when units are in meters) g=16 (when units are in feet) t=time h(t)=height π£ 0 =initial velocity β 0 =initial height π£ 0
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http://phet. colorado. edu/sims/projectile-motion/projectile-motion_en
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Assignment #5 Pg. 52 #1-11 odd, all, odd, 43, 44
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