graphing simple quadratics y = ax 2 + c objective: students will graph simple quadratic functions
DESCRIPTION
Graph y = 3x 2 and Compare your results with the Parent Function 1)Make an x-y table 2)Pick any values for x 3)Solve for y for each x 4)Place ordered pairs on the graph xy When a > 1 the graph is narrowerTRANSCRIPT
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Graphing Simple Quadraticsy = ax2 + c
Objective: Students will graph simple quadratic functions
![Page 2: Graphing Simple Quadratics y = ax 2 + c Objective: Students will graph simple quadratic functions](https://reader036.vdocument.in/reader036/viewer/2022082415/5a4d1ada7f8b9ab0599747eb/html5/thumbnails/2.jpg)
Graph the Parent Functiony = x2
1) Make an x-y table2) Pick any values for x3) Solve for y for each
x4) Place ordered pairs
on the graphx y
-2-1012
41014
![Page 3: Graphing Simple Quadratics y = ax 2 + c Objective: Students will graph simple quadratic functions](https://reader036.vdocument.in/reader036/viewer/2022082415/5a4d1ada7f8b9ab0599747eb/html5/thumbnails/3.jpg)
Graph y = 3x2 and Compare your results with the Parent Function
1) Make an x-y table2) Pick any values for x3) Solve for y for each
x4) Place ordered pairs
on the graphx y
-2-1012
1230312
When a > 1 the graph is narrower
![Page 4: Graphing Simple Quadratics y = ax 2 + c Objective: Students will graph simple quadratic functions](https://reader036.vdocument.in/reader036/viewer/2022082415/5a4d1ada7f8b9ab0599747eb/html5/thumbnails/4.jpg)
Graph y = -1/4x2 and Compare your results with the Parent Function
1) Make an x-y table2) Pick any values for x3) Solve for y for each
x4) Place ordered pairs
on the graphx y
-4-2024
-4-10-1-4 Because a is negative the graph is reflected and
when a < 1 then the graph is wider
![Page 5: Graphing Simple Quadratics y = ax 2 + c Objective: Students will graph simple quadratic functions](https://reader036.vdocument.in/reader036/viewer/2022082415/5a4d1ada7f8b9ab0599747eb/html5/thumbnails/5.jpg)
Graph y = x2 + 5 and Compare your results with the Parent Function
1) Make an x-y table2) Pick any values for x3) Solve for y for each
x4) Place ordered pairs
on the graphx y
-2-1012
96569
When a value is added (or subtracted) to x2 the graph moves up (or down) but is the same graph as the parent function
![Page 6: Graphing Simple Quadratics y = ax 2 + c Objective: Students will graph simple quadratic functions](https://reader036.vdocument.in/reader036/viewer/2022082415/5a4d1ada7f8b9ab0599747eb/html5/thumbnails/6.jpg)
Match the Quadratic Function with its Graph
1. Y = x2 - 4 2. Y = -x2 + 4 3. Y = 4x2 – 44. Y = ¼ x2 - 4
C
A B
D E
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• Write at least one sentence to describe difference between the given function and the Parent Function y = x2
1) Y = 7x2
2) Y = -x2
3) Y =x2 – 7 4) Y = 1/2x2
5) Y = 1/5x2 + 2
![Page 8: Graphing Simple Quadratics y = ax 2 + c Objective: Students will graph simple quadratic functions](https://reader036.vdocument.in/reader036/viewer/2022082415/5a4d1ada7f8b9ab0599747eb/html5/thumbnails/8.jpg)
• Sailors need to consider the speed of the wind when adjusting sails on their boat. The force f (in pounds per square foot) on a sail when the wind is blowing perpendicular to the sail can be modeled by the function f = 0.004v2 where v is the wind speed ( in knots).
a) Graph the function for wind speed from 0 to 50 knots.b) Use the graph to estimate the wind speed that will
produce force of 1 pound per square foot on a sail.c) Estimate the wind speed that will produce a force of 5
pounds per square foot.
![Page 9: Graphing Simple Quadratics y = ax 2 + c Objective: Students will graph simple quadratic functions](https://reader036.vdocument.in/reader036/viewer/2022082415/5a4d1ada7f8b9ab0599747eb/html5/thumbnails/9.jpg)
In the Giant Redwood forest a pinecone falls about 144 feet from the branch of a pine tree. Its height (in feet) can be modeled by the function h(t) = -16t2 + 144, where t is the time in seconds.
a) Graph the function.b) At what height is the
pinecone at 1 second.c) At what height is the
pinecone at 2 seconds.d) After how many seconds
does the pinecone hit the ground