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Graphing

Graphing. Graph:. NOTE: Here are some more like this: y = x y = 1.2 x y = 1/3 x y = 4 x. y = - 3x. THEY ALL HAVE A “x” and a “ y “ but NOTHING added or subtracted to them. x = (0,0). y = (0,0). MAKE a “t” chart to help you graph this type. m = -3. y. x. -3 -6 -9. 1 2 3.

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Graphing

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  1. Graphing

  2. Graph: NOTE: Here are some more like this: y = x y = 1.2 x y = 1/3 x y = 4 x y = - 3x THEY ALL HAVE A “x” and a “ y “ but NOTHING added or subtracted to them x = (0,0) y = (0,0) MAKE a “t” chart to help you graph this type m = -3 y x -3 -6 -9 1 2 3

  3. Graph: NOTE: IT DOES NOT have an “x” ! y = -4 x = none y = (0,4) m = 0

  4. Graph: NOTE: IT DOES NOT have an “y” ! x = -3 x = (-3,0) y = none m = undefined

  5. Solve for y: NOTE: This is NOT the same as “find the y intercept”! y-2 = - 3(x+2) Distribute the - 3 y-2 = - 3x + - 6 Add 2 to both sides y = - 3x + - 4 DONE

  6. Find the y intercept: LET x = 0 and evaluate! y-2 = - 3(x+2) y-2 = - 3(0+2) y-2 = - 3(2) y-2 = - 6 HEY!!! What is the slope of this line? y = - 4

  7. Consider…. 4x – 6y = 36 You’re finding the y intercept because you let x equal zero! If I do this next step….what am I finding? Why? 4(0) – 6y = 36 If you find the x and y intercepts you can use the SLOPE FORMUAL OR…. What is the slope of this linear equation? You could solve for y and get this standard form into the slope intercept form! m: 4/6 or 2/3

  8. Consider…. It graphs a parabola BECAUSE the degree of the polynomial is a 2! y = - 4(x – 3)2 What does this graph? How do you know that? It flips DOWN because the 4 is NEGATIVE! Does this graph flip up or down? How do you know this? What are the coordinates of it’s vertex? (3, 0) Find it’s x intercept(s)? 0 = - 4(x – 3)2 0 = - 4(x – 3)2 Divide both sides by -4 and then square root both sides. 0 = x – 3 Add 3 to both sides. x-intercept is (3,0)

  9. Consider…. It graphs a parabola BECAUSE the polynomial has TWO x’s! y = (x + 4)(x – 3) What does this graph? How do you know that? Because it is factored AND equal to zero, we can set both factors equal to zero and solve! Find the x intercepts 0 = (x + 4)(x – 3) 0 = (x + 4) 0 =(x – 3) x = -4 x =3 X: (-4, 0) (3, 0)

  10. Add the x intercepts together and divide by 2! y = (x + 4)(x – 3) How can you find the vertex IF you KNOW the x intercepts? This gives you the x-coordinate of the vertex. Substitute this value into the equation to determine the y-coordinate. = (- -11.25 y = (1/2 + 4)(1/2 – 3) y = (1/2 + 4)(1/2 – 3) y = -11.25

  11. Consider…. Either factoring or Q.F. y = x2 + x - 12 What “tools” would you use to find the x intercepts? Because it’s a trinomial, the leading coefficient is 1 it is easy to factor! y = (x + )(x+ ) -3 4 We need two factors of – 12 that add to 1 4 and – 3 multiply to -12 and ADD to 1 To finish this one, we would set the factors equal to zero and solve the equations! Just like we did on the quadratic before this one!

  12. Consider…. Either factoring or Q.F. y = 5x2 + x - 2 What “tools” would you use to find the x intercepts? It doesn't factor so What does it mean if the determinate turns out to be NEGATIVE? That there are NO real x-intercepts!!!

  13. MORE WILL BE ADDED to this PPT so check back! so check back!

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