1. Quadratics 2
Write Equations, Match graphs and equations, describe a graph and identify parts of a graph

2. Identify if Equations is quadratic
Think of you definition – look for a degree 2 polynomial, one variable squared
You may need to FOIL or distribute to determine if it is quadratic

3. Example
x(x+2) yes because when you distribute the x is squared (x+3)+(x-3) no because this is addition not multiplication

4. Identify if a table is quadratic
Put table in order
Look for pattern in the dependent variable
Look for a pattern in the pattern – this is where you determine it is a quadratic

5. Example
Since second pattern is the same it is quadratic

6. Determine the equation from a table
Determine if it is a quadratic
2 methods
If you have the x intercepts
Look at table if you have both x-intercepts, y=0
(X ___ ) (X ____ ) sub in the opposite of the x values in the table into the blanks, include the sign
If you have the y intercept
Look at table for when x=0, this is y intercept
Pick another ordered pair
Substitute the values into the standard form of a quadratic
y= x2 + bx +c, c is the constant b is what you are trying to figure out
Once values are substituted in you could calculate the b value and then write the equation in expanded form

7. Example -8 -6 -4 -2 0 2 4 6 2 2 2 2 2 2 2 Y = (x+1)(x-2) Y=x2 + bx -2
Y = (x+1)(x-2)
Y=x2 + bx -2
4= (3)^2 + b(3) -2
4=9 + 3b -2
-3=3b
-1=b
Y=x2 -1x -2

8. Describe a graph Identify the vertex Identify the x and y intercept
Write equation for axis of symmetry
State if it opens up or down

9. Example
Vertex (7.5, 56) this is Approximate X-int (0,0) and (15,0) Y-int (0,0) Axis of sym X=7.5 Opens down

10. Describe an Equation
Know how to factor and expand each will give you some information
Y intercept – you find this in standard form, the constant value
X intercepts – factor into 2 binomials, take the opposite of the values inside the ( )
Vertex – find the midpoint between the x-intercepts (average of x values), sub this value into the equation and solve for y
Write the equation for the axis/line of symmetry

11. Example
Y-int is (0,15) X-int (-3,0) and (-5,0) Vertex = 2/2=1 (1)^2+8(1) =24 Vertex (1,24) Axis of sym x=1

12. Sketch a Graph Find the vertex Find the x and y intercepts
Plot on a coordinate system and connect with a curve