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# Polynomial Graphing Lesson

Short lesson on graphing polynomials.
Published on: Mar 4, 2016
Published in: Education

#### Transcripts - Polynomial Graphing Lesson

• 1. Graphing Polynomials
• 2. Rearrange the Equation • 2y – 2x2 – 12x= 18 • Add 4x2 to each side • Add 12x to each side • 2y= 2x2 + 12x + 18 • Divide by 2 • y= x2 + 6x + 9
• 3. Find theVertex • With equation in y= Ax2 + Bx + C form, x-coordinate =-B/2A • X-coordinate= -6/2 = -3 • Plug -1/3 into equation to find y • (-3)2 + 6(-3) + 9 = 9 – 18 + 9 = 0
• 4. Find Intercepts • X intercept is found when y=0 (happens to be the vertex) • Often you will have to factor, and get 2 results. • In this case, y=(x+3)2 • Y intercept is found when x=0 • Y= (0)2 + 6(0) + 9 = 9
• 5. Find Other Easy Points • Try x=1, x= -1, for instance • Or 1 to either side of the vertex • In this case, x= -2, x=-4
• 6. Connect Points with Curve
• 7. Check End Behavior • Check to see if the graph looks how it should • Even powered functions will have their ends pointing the same direction • If the variable in front of the x2 is positive they will both point up • If the variable in front of the x2 is negative they will both point down • We see that this is consistent with our graph
• 8. Now try these on your own • x-y= 2-x2 • x2 – 4 = y - 3x • 6 – x=x2 + y
• 9. Here’s a video to help explain more
• 10. Recap • Rearrange the equation so that y is isolated on one side • Find the vertex (-b/2a) • Graph the intercepts [ (0,y) (x,0)] • Find a few other points • Draw smooth curve • Check with end behavior