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3 FORMS OF GRAPHING

VERTEX FORM  y=a(x-h)^2+k

TO KNOW WHAT VERTEX FORM IS, YOU NEED TO KNOW 4 IMPORTANT THINGS

 

  • THE FORMULA

  • THE STEP PATTERN

  • HOW TO GRAPH IT

  • PROPER TERMINOLOGY

WHAT IS THE STEP PATTERN?

 

 

 

 

 

If you take the "standard" parabola, y = x², which has it's vertex at the origin (0, 0), then: 

Starting from the vertex (0,0) as "the first point" ... 

OVER 1 (right or left) from the vertex point, UP 1² = 1 from the vertex point 
OVER 2 (right or left) from the vertex point, UP 2² = 4 from the vertex point

 

ALWAYS remember this pattern!

 

 

EXAMPLE--> OVER 1, UP 1 (FROM VERTEX)                           OVER 2, UP 4

 

 

 

 

 

THINGS TO REMEMBER:

  • The step pattern will be affected if there is a vertical stretch

  • The vertical stretch can be negetive or positive 

 

 

 

 

 

 

FACTORED FORM y=(x-r)(x-s)

Factored form looks like; y=a(x-s)(x-t)

 

The form of an algebraic expression in which no part of the expression can be made simpler by pulling out a common factor.

In factored form, there are two x intercepts (s&t)

EX: y=-2(x+3)(x+1)

x intercepts @ (-3,0)(-1,0)

(-3+-1)/2

Therefore; the axis of symmetry is -2.

 

 

 

 

How to graph factored form:

You need;

  • a vertex

  • two points

If the axis of symmetry (the x value) is -2, to find what y is, just plot the x value into the equation and make y=0

therefore; it would be y=-2(-2+3)(-2+1)

=-2(1)(-1)

Y=2

y=-2(x+3)(x+1)

vertex@ (-2,2)

two points;(-1,0) & (-3,0)

 

Now all you have to do is plot the vertex and the points and draw your parabola

GRAPHING FROM VERTEX FORM

STANDERED FORM y=ax^2+bx+c

Standard Form

The Standard Form of a Quadratic Equation looks like this:

y=ax^2+bx+c

 

 

    • a, b and c are known values. a can't be 0.

    • "x" is the variable or unknown (we don't know it yet

Standered form cannot be graphed

So how do we graph it? 

 

CONVERT STANDERED FORM TO VERTEX FORM

MAXIMA AND MINIMA

 

We've determined that we cannot graph standered form. So how do we change it to vertex form?

We complete a perfect square!

 

"Plus Minus"

THE QUADRATIC FORMULA

How do these three forms relate?

 As you can see the direction of opening is the same for all forms. The variables are the same but written differently. You just solve for certain values such as the vertex, optimal value, etc in a different way!

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