Graphing

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

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

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

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

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

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

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

y = (x + 4)(x – 3) Consider…. What does this graph? How do you know that? It graphs a parabola BECAUSE the polynomial has TWO x’s! 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)

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

y = x 2 + x - 12 Consider…. What “tools” would you use to find the x intercepts? Either factoring or Q.F. We need two factors of – 12 that add to 1 y = (x + )(x+ ) Because it’s a trinomial, the leading coefficient is 1 it is easy to factor! 4 and – 3 multiply to -12 and ADD to 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!

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

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