05 Quadratics - Graphing The Parent Function 1

Quadratics – Manipulating the Parent Function Discovery Lesson If you take the following steps in the order they are given, you should have full understanding of graphing quadratics by the end of class. Please don’t rush through all of the parts. 1. We will begin with f  x   x2 , the most basic of quadratic functions. We call this the parent function. a. In the table provided, fill in the values of x into the parent function to find the corresponding values of f(x). f  x   x2 x f  x

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b. Graph your points on the grid provided, and then connect them.

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c. Now turn on your graphing calculator, and go to ‘y =’. Plug in y1  x 2 . Go to ‘zoom’ and choose ‘standard’. Does your graph match the one above? If not, check your points.

Quadratics – Manipulating the Parent Function Discovery Lesson 2. Vertical Shift of the Parent Function ( f  x   x2  k ).

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a. Fill in the chart for f  x   x2  2 , and plot the points on the graph provided. f  x   x2  2 x f  x

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b. What’s the difference between this graph and the parent graph from 1.b?

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Go to ‘y=’ and plug in y2  x 2  2 . Press ‘graph’. Did you graph it correctly? If not, check your values?

d. Fill in the chart for f  x   x2 1 , and plot the points on the graph.

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f  x   x2 1 x f  x

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e. Go to ‘y=’ and plug in y3  x 2  1 . Check your graph. f. What is the general effect of k on f  x   x2  k ?

Quadratics – Manipulating the Parent Function Discovery Lesson 3. Horizontal Shift of the Parent Function ( f  x    x  h  ). 2

a. Fill in the chart for f  x    x  2  , and plot the points, then check your 2

graph on the calculator.

f  x    x  2 x f  x

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b. Fill in the chart for f  x    x  1 , and plot the points. Then check your 2

graph on the calculator.

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f  x    x  1 x f  x

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c. What is the general effect of h on f  x    x  h  ? 2

Quadratics – Manipulating the Parent Function Discovery Lesson 4. Widening and Narrowing the Parent Function. ( f  x   ax2 ). a. Fill in the table for f  x   2x2 , plot the points, and check the calculator.

f  x   2 x2 x f  x

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b. Fill in the table for f  x    12 x2 , plot the points, and check the calculator.

f  x    12 x2 x f  x

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c. What is effect of a on f  x   ax2 ? 5. Challenge: Graph f  x   3  x  1  5 .

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2

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