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

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

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

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

Example -8 -6 -4 -2 0 2 4 6 2 2 2 2 2 2 2 Since second pattern is the same it is quadratic

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

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 -8 -6 -4 -2 0 2 4 6 2 2 2 2 2 2 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

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

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

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

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

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