We determine the polynomial function, f(x), with the least possible degree using 1) turning points 2) The x-intercepts ("zeros") to find linear factors 3) Multiplicity of each factor 4) The leading coefficient to produce the given y-intercept. (Time stamps below) 1) If "n" is the number of turning points, then "n+1" is the least possible degree of f(x). 00:55 2) Use the x-intercepts to determine the factors If x = a is the location of an x-intercept, then ( x - a ) will be a linear factor of f( x ) 01:31 3) Use the behavior of the graph to determine the multiplicity of each factor 03:29 If graph "goes through" the x-axis where x = a, then ( x - a ) is a factor with an odd multiplicity. "bounces" at the x-axis where x = a, then ( x - a ) is a factor with an even multiplicity. 4) Use the y-intercept of the graph to determine the leading coefficient, "a" 06:28 Add a constant "a" to the function and plug in the point (0, f(0) ) to solve for "a".
Basically you Plug the y-intercept into the equation. For this function the y-intercept is the point (0, 4)…..( X= 0, y = 4)….since “f(x)” is another way to say “y”…the equation is y = a(x+4)(x-2)^2…..put x=0 and y= 4 into that and solve for a. There are websites that can show you how to solve that step by step. I skipped a few steps in the video.
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We determine the polynomial function, f(x), with the least possible degree using 1) turning points 2) The x-intercepts ("zeros") to find linear factors 3) Multiplicity of each factor 4) The leading coefficient to produce the given y-intercept. (Time stamps below)
1) If "n" is the number of turning points, then "n+1" is the least possible degree of f(x).
00:55
2) Use the x-intercepts to determine the factors
If x = a is the location of an x-intercept, then ( x - a ) will be a linear factor of f( x )
01:31
3) Use the behavior of the graph to determine the multiplicity of each factor
03:29
If graph
"goes through" the x-axis where x = a, then ( x - a ) is a factor with an odd multiplicity.
"bounces" at the x-axis where x = a, then ( x - a ) is a factor with an even multiplicity.
4) Use the y-intercept of the graph to determine the leading coefficient, "a"
06:28
Add a constant "a" to the function and plug in the point (0, f(0) ) to solve for "a".
You made it extremely easy to understand, great presentation!
Thank you so much for the comment! Glad it was helpful.
Thank you for making this ❤❤
You're very welcome. Glad it was helpful and I appreciate you taking the time to comment.
Well explained....Thanks...!!!
Thank you so much! Glad it was helpful!
Tysm
you're welcome.
Ready for my quiz. Thank you!
Awesome. Hope it went well
Did you record this 10 feet away from your mic???
No.
@@SulockMath yes you did
@@bimg1915 wrong
How did you get a??
Basically you Plug the y-intercept into the equation. For this function the y-intercept is the point (0, 4)…..( X= 0, y = 4)….since “f(x)” is another way to say “y”…the equation is y = a(x+4)(x-2)^2…..put x=0 and y= 4 into that and solve for a. There are websites that can show you how to solve that step by step. I skipped a few steps in the video.