Graphing

Graph:

y = - 3xNOTE: Here are some more like this:y = x y = 1.2 xy = 1/3 xy = 4 x

THEY ALL HAVE A “x” and a “ y “ but NOTHING added

or subtracted to themx = (0,0)y = (0,0)

m = -3MAKE a “t” chart to help

you graph this type

x y

123

-3-6-9

Graph:

y = -4NOTE: IT DOES NOT

have an “x” !

x = noney = (0,4)

m = 0

Graph:

x = -3NOTE: IT DOES NOT

have an “y” !

x = (-3,0)y = nonem = 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 + - 6 Add 2 to both sides

y = - 3x + - 4 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 = 36Consider….

4(0) – 6y = 36If 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)2Consider….

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

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 =3X: (-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 = (1/2 + 4)(1/2 – 3)

y = -11.25

-11.25

y = x2 + x - 12Consider….

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 1

4 -3

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 = 5x2 + x - 2Consider….

What “tools” would you use to find the x intercepts?

Either factoring or

Q.F.

It doesn't factor so 𝑥= −𝑏±√𝑏 2

−4𝑎𝑐2𝑎What does it mean if the determinate turns out to be NEGATIVE?

That there are NO real x-intercepts!!!

MORE WILL BE ADDED to this PPT

so check back! so check back!