UNIT 1: QUADRATICS Final Exam Review

TOPICS TO COVER  GCF  Factoring  Solving Quadratic Equations  Graphing Quadratic Equations  Projectile Motion

GCF  GCF stands for GREATEST COMMON FACTOR  When finding the GCF of terms, follow these steps:  Find the LARGEST number that the 2 terms have in common and take it out  Find the largest amount of VARIABLES that the 2 terms have in common and take it out  To write what is left over, start with the NUMBERS, and then finish with the VARIABLES

GCF  Try this one now: Factor out the GCF of 16x 4 y 3 – 24x 2 y

FACTORING  Factoring helps you to find where a function crosses the X AXIS  Steps to follow when factoring  Draw an X  For the number on the top of the X, MULTIPLY the FIRST number by the LAST number  For the number on the bottom of the X, write the MIDDLE number  Figure out which 2 numbers will MULTIPLY to get the top number on the X and ADD to get the bottom number on the X  SPLIT THE MIDDLE by rewriting your equation with the 2 numbers that you found on the X.  Group the FIRST 2 TERMS and the LAST 2 TERMS.  Take out the GCF of the first 2 terms and the last 2 terms  Use your GCF and what was left over to write your equation in factored form

FACTORING  Watch this Video for an example

FACTORING  Try this one now: Factor 6x 2 – 13x + 2

SOLVING QUADRATIC EQUATIONS  Solving Quadratic Equations allows you to solve for x.  Steps to follow when solving quadratic equations:  Make sure the equation is equal to 0. If not, move everything over to the left side so that the equation does equal 0.  Factor  Set each factor equal to 0 and then SOLVE for x  Most of the time, there will be 2 answers.

SOLVING QUADRATIC EQUATIONS  Watch this Video for an example

SOLVING QUADRATIC EQUATIONS  Try this one now: Solve for X: 5x 2 + 8x + 3 = 0

GRAPHING QUADRATIC EQUATIONS  Graphing Quadratic Equations helps you to find symmetry, zeros, and the vertex.  Steps to graph a quadratic equation:  Start by putting the equation into your calculator by pressing the “y=“ button  Look at the table to get some points to graph  Connect the points

GRAPHING QUADRATIC EQUATIONS  To find the zeros, look for where the y value is 0  To find the vertex, look where the y values start to REPEAT themselves  To find the axis of symmetry, find the VERTEX, and the line will be the X VALUE of the vertex.

GRAPHING QUADRATIC EQUATIONS  Example: x 2 + 4x = 0 Zeros: x = -4, x = 0 Vertex: (-2, -4) Axis of Symmetry: x = -2

GRAPHING QUADRATIC EQUATIONS  Try this one now: Graph: x 2 + 2x – 3 Find the: 1.Zeros 2.Vertex 3.Axis of Symmetry

PROJECTILE MOTION  Projectile Motion uses word problems to find MAXIMUM HEIGHTS and the DISTANCE that something travels.  Steps to take to find the MAXIMUM  Put the function in your calculator  Press “2 nd ” and “TRACE” and choose “MAXIMUM”  Move your cursor so that it is to the LEFT of the maximum and hit “Enter”  Then move your cursor so that it is to the RIGHT of the maximum and hit “Enter”  Then hit “Enter” one more time  The maximum is the Y VALUE in the answer.

PROJECTILE MOTION  Projectile Motion uses word problems to find MAXIMUM HEIGHTS and the DISTANCE that something travels.  Steps to take to find the DISTANCE TRAVELED  Put the function in your calculator  Press “2 nd ” and “TRACE” and choose “ZERO”  Move your cursor so that it is to the LEFT of the place where the function crosses the x axis and hit “Enter”  Then move your cursor so that it is to the RIGHT of the place where the function crosses the x axis and hit “Enter”  Then hit “Enter” one more time  The distance traveled is the X VALUE in the answer.

PROJECTILE MOTION

ALL DONE!