Algebra I Unit 3A Notes Modeling and Analyzing Quadratic

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Standard What am I learning Mastery,MGSE9 12 F IF 4 Using tables graphs and. verbal descriptions interpret the key,characteristics of a function which models. the relationship between two quantities,How to describe characteristics of a. Sketch a graph showing key features, including intercepts interval where the quadratic function vertex extrema axis of. function is increasing decreasing positive symmetry intercepts intervals of change. or negative relative maximums and domain range and end behaviors. minimums symmetries end behavior and,periodicity,MGSE9 12 F IF 5 Relate the domain of a.
function to its graph and where,applicable to the quantitative relationship. it describes For example if the function,h n gives the number of person hours it. takes to assemble n engines in a factory,then the positive integers would be an. appropriate domain for the function How to describe the characteristics of a. MGSE9 12 F IF 7 Graph functions expressed 3A 2 quadratic function in the context of a real. algebraically and show key features of the world scenario. graph both by hand and by using,technology,MGSE9 12 F IF 7a Graph linear and. quadratic functions and show intercepts,maxima and minima as determined by.
the function or by context,MGSE9 12 F IF 6 Calculate and interpret. the average rate of change of a function, presented symbolically or as a table over How to calculate the quadratic average. a specified interval Estimate the rate of 3A 3 rate of change using a specific interval in. change from a graph Analyze functions an equation or graph. using different representations,MGSE9 12 F BF 3 Identify the effect on the. graph of replacing f x by f x k k f x,f kx and f x k for specific values of. k both positive and negative find the, value of k given the graphs Experiment How to describe the transformations of a.
with cases and illustrate an explanation of quadratic in vertex form. the effects on the graph using technology,Include recognizing even and odd. functions from their graphs and algebraic,expressions for them. MGSE9 12 F IF 7 Graph functions expressed, algebraically and show key features of the 3A 5 How to graph a quadratic in vertex form. graph both by hand and by using,technology, MGSE9 12 F IF 7a Graph linear and How to graph a quadratic in standard. quadratic functions and show intercepts form,maxima and minima as determined by.
the function or by context How to convert between vertex and. standard forms,How to use the graph a quadratic to. answer application questions,MGSE9 12 F IF 9 Compare properties of two. functions each represented in a different,way algebraically graphically numerically. How to compare the characteristics of,in tables or by verbal descriptions For 3A 9. example given a graph of one function quadratic functions. and an algebraic expression for another,say which has the larger maximum.
Introduction to Quadratics, A quadratic function is a function that has an term in it somewhere. Determine whether each function is linear or quadratic. a Y 3x 5 b Y 3x x 5 c Y x 2 x 4 d Y 6x 5 2x, Quadratic Functions y x2 when graphed are or U shaped graphs. Parent Function,Two Major Forms of a Quadratic,Standard y ax2 bx c Vertex y a x h 2 k. If a is The graph opens,If a is The graph opens,Which direction would each quadratic open. Example 1 y 2x2 x 7 Example 2 y x 5 2 9,Example 3 y 3 x 1 2 4 Example 4 y 6x2 7.
Characteristics of Quadratics,Characteristic Definition Example. The lowest or the highest point,on the parabola,For a quadratic this point. will be the,The lowest point y value on,the parabola. The highest point y value on,the parabola,The vertical line that divides. the parabola into mirror,images and goes through the.
When describing the AOS,always use the value,of the vertex written in an. equation x,All possible values of x,All possible values of y. Where the graph crosses the y,axis written 0 y,If you do not see one on. the graph plug in 0 for x into,Where the graph crosses the x. axis written x 0,You might have 0 1 or 2,points of intersection.
Other names are,The direction each end,approaches as the x values. approach positive and negative, Describe the characteristics of the following graphs. Vertex Axis of Symmetry,Extrema Max Min Value,Domain Range. a Y Intercept,X Intercepts Zeros,End Behavior As x y. Vertex Axis of Symmetry,Extrema Max Min Value,Domain Range.
a Y Intercept,X Intercepts Zeros,End Behavior As x y. More Characteristics,Characteristic Definition Example. The part of the graph,that is increasing as,you read from LEFT. TO RIGHT on the,The part of the graph,that is decreasing as. you read from LEFT,TO RIGHT on the, Label the coordinates of your extrema Put the X VALUES on the number line.
Then find the intervals of increase and decrease for the graph below. Intervals of Increase,Intervals of Decrease, Describe the characteristics of the following graphs. Vertex Axis of Symmetry,Extrema Max Min Value,Domain Range. a Y Intercept,X Intercepts Zeros,Int of Increase,Int of Decrease. End Behavior As x y,Example 2 Vertex Axis of Symmetry. Extrema Max Min Value,Domain Range,a Y Intercept,X Intercepts Zeros.
Int of Increase,Int of Decrease,End Behavior As x y. Example 3 Vertex Axis of Symmetry,Extrema Max Min Value. Domain Range,a Y Intercept,X Intercepts Zeros,Int of Increase. Int of Decrease,End Behavior As x y,Average Rate of Change. The average of slopes over a given interval To calculate you need 2 points 2 x s and. their corresponding y s,RoC m 2 1 2 1, The first y value you get when you use your first x value using a graph.
table or equation, The second y value you get when you use your second x value using a. graph table or equation, Example 1 Calculate the average rate of change using the. interval 2 x 0, Example 2 Calculate the average rate of change using the. interval 0 x 1, Example 3 Calculate the average rate of change using the. interval 2 x 1, Example 4 Calculate the average rate of change using the interval 2 x 0.
Example 5 Calculate the average rate of change using the interval 1 x 4. Example 6 Calculate the average rate of change using the interval 2 x 0. Example 7 Calculate the average rate of change using the interval 8 x 4. Describe the characteristics of the following graphs. Vertex Axis of Symmetry,Extrema Max Min Value,Domain Range. a Y Intercept,X Intercepts Zeros,Int of Increase,Int of Decrease. End Behavior As x y,Rate of change on the interval 1 x 3. Example 9 Vertex Axis of Symmetry,Extrema Max Min Value. Domain Range,a Y Intercept,X Intercepts Zeros,Int of Increase.
Int of Decrease,End Behavior As x y,Rate of change on the interval 1 x 3. Example 10, Given the equation 3 2 4 5 calculate the average rate of change using the. interval 1 x 7,Vertex Form of a Quadratic,3 2 2 4 2 5 2 3 2 4. Vertex Opens Vertex Opens Vertex Opens,1 1 3 1 2 6. 1 2 4 2 2 5,Vertex Opens,Vertex Opens Vertex Opens.
1 5 4 2 1 1 2,Vertex Opens,Vertex Opens Vertex Opens. What patterns did you notice from the equation and the graph. VERTEX FORM,Vertex If a 0 opens If a 0 opens, For the following equations identify the vertex and whether the graph opens up or down. 1 2 3 2 8 3 4 9 2,V Opens V Opens,2 3 2 5 4 3 5 7,V Opens V Opens. Transformations of Quadratics, A is the original graph of a function WITHOUT any transformations For quadratics the. equation of the parent function is y, The best form to describe the transformations of a quadratic is.
Type of Looks Examples,Transformation Like from f x x2. Vertical Shift add or subtract a constant g x f x k. outside of the parent function,Adding moves the function up and subtracting. moves it down g x f x k, Horizontal Shift add or subtract a constant with g x f x h. the x value or inside the parent function,Adding moves the function left and subtracting. moves it right g x f x h, Reflection over X Axis multiply the parent g x f x.
function by a 1 or put a negative in front of the,coefficient of the function. Vertical Stretch multiply the parent function by g x a f x. a constant that is greater than 1,IGNORE THE NEGATIVE SIGN. Vertical Shrink multiply the parent function by g x a f x. a constant that is more than 0 but less than 1,IGNORE THE NEGATIVE SIGN. For each of the following equations identify the vertex and direction the graph opens. Then list ALL transformations,Vertex Transformations. Vertex Transformations,Vertex Transformations,Vertex Transformations.
Vertex Transformations,Vertex Transformations,Vertex Transformations. Vertex Transformations,Vertex Transformations,Graphing Quadratics from Vertex Form. VERTEX FORM,Vertex If a 0 opens If a 0 opens,To graph a quadratic in VERTEX FORM. 1 Find the vertex Identify whether the graph should open up or down. 2 Create a table Put the vertex as the CENTER VALUE of the table. 3 Fill in your table with the two values of x that come before and after the x value of your vertex. 4 Plug all x values into your equation to find the y value that goes with them. If done correctly the y values should have a PATTERN. The 1st and 5th y values should match So should the 2nd and 4th y values. Example 1 3 2 5,VERTEX X Y,Example 2 2 4 2 7,VERTEX X Y. Graph each of the following quadratic functions Find the characteristics of your graph. 1 3 2 1 2 2 2 4,Vertex Opens Vertex Opens,Domain Range Domain Range.
Zeroes Y Int Zeroes Y Int,Increase Decrease Increase Decrease. End Behavior As x f x End Behavior As x f x,As x f x As x f x. 3 2 5 2 4 2 2 2,Vertex Opens Vertex Opens,Domain Range Domain Range. Zeroes Y Int Zeroes Y Int,Increase Decrease Increase Decrease. End Behavior As x f x End Behavior As x f x,As x f x As x f x.
Converting Quadratics from Vertex to Standard Form. Let s Review How did we multiply a binomial by a binomial. Ex 1 2x 7 3x 1 Ex 2 2x 5 x 3 Ex 3 2x 3 2,To convert from VERTEX FORM to STANDARD FORM. 1 Rewrite the squared term as 2 BINOMIALS, 2 Multiply the BINOMIALS Combine all like terms to create an expression. 3 Place the expression from the binomials back in a parentheses behind the a value. 4 DISTRIBUTE a to the expression IN PARENTHESES DO NOT DISTRIBUTE to a value OUTSIDE the parentheses. 5 Add any values outside the parentheses to the expression. Example 1 3 2 8 Example 2 2 4 2 1,Vertex Y Int Vertex Y Int. Example 3 7 2 Example 4 2 8 2 14,Vertex Y Int Vertex Y Int. Algebra I Unit 3A Notes Modeling and Analyzing Quadratic Functions Graphs Name Important Dates Quiz 1 Thursday March 19th Transformations and Characteristics of Quadratics Quiz 2 Monday March 23rd Graphing and Converting in Vertex and Standard Form TEST Wednesday March 25th

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