MS Algebra Ch Graph ax 2 + bx + c. Mr. Deyo
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1 MS Algebra Ch Graph ax 2 + bx + c Mr. Deyo
2 Learning Target By the end of the period, I will graph quadratic equations in the standard form of y = ax 2 + bx + c. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.
3 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section TxtBk. Problems 3) Section Notes Copied on blank sheet of paper in Binder? Solved and Put in Binder? Table of Contents Date Description Date Due
4 Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1. How are the two images similar? 2. How are they different? 3. How can these two images be related to math?
5 Vocabulary 1) Parabola ( y = ax 2 + bx + c ) 2) Axis of Symmetry x = -b 3) Vertex 2a 4) X-Intercept (Roots) (X,0) 5) Discriminant ( b 2-4ac )
6 Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example Word List Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing
7 Daily Warm-Up Exercises For For use use with with pages pages xxx xxx Evaluate the expression. 1. x 2 2 when x = x when x = 2
8 Daily Warm-Up Exercises For For use use with with pages pages xxx xxx Evaluate the expression. 1. x 2 2 when x = 3 ANSWER x when x = 2 ANSWER 17
9 Notes: y = ax 2 + bx + c 1) Axis of Symmetry x = -b 2a 2) Vertex (, Y) 3) Y-Intercept ( 0, Y) 5) Discriminant b 2 4ac b 2 4ac > 0 2 roots b 2 4ac = 0 1 roots b 2 4ac < 0 0 roots 6) If a is positive 4) X-Intercepts (Factors/Roots) 7) If a is negative
10 Example 1 Problem A X-Intercept(s): y = -2x x - 7 Axis of Symmetry: a= b= c= Vertex: x y Y-Intercept:
11 Example 1 Find the axis of symmetry and the vertex Consider the graph of the function y = 2x x 7. a. Find the axis of symmetry. b. Find the vertex. SOLUTION y = 2x x 7, a = 2 b = 12. a. For the function and b x = = 12 2a 2 ( 2) = 3 Substitute 2 for a and 12 for b. Then simplify.
12 Example 1 Find the axis of symmetry and the vertex ANSWER The axis of symmetry is the vertical line x 3. = b b. The x-coordinate of the vertex is, or 3. 2a To find the y-coordinate, substitute 3 for x in the function and simplify. y = 2( 3) ( 3) 7 = 11 Substitute 3 for x. Then simplify. ANSWER The vertex is ( ). 3, 11
13 Example 2 Problem B X-Intercept(s): y = 3x 2-6x + 2 Axis of Symmetry: a= b= c= Vertex: x y Y-Intercept:
14 Example 2 Graph y = ax 2 Graph y = 3x 2 6x bx + c STEP 1 Determine whether the parabola opens up or down. Because a > 0, the parabola opens up. STEP 2 STEP 3 Find and draw the axis of symmetry: b x = = 6 =1 2a 2( 3) Find and plot the vertex. The x-coordinate of the vertex is b, or 1. 2a
15 Example 2 Graph y = ax 2 + bx + c To find the y-coordinate, substitute 1 for x in the function and simplify. y = 3( 1) 2 6 ( 1 ) + 2 = 1 So, the vertex is ( 1, 1). STEP 4 Plot two points. Choose two x-values less than the x-coordinate of the vertex. Then find the corresponding y-values. x 0 1 y 2 11 STEP 5 STEP 6 Reflect the points plotted in Step 4 in the axis of symmetry. Draw a parabola through the plotted points.
16 Example 1 Guided Practice X-Intercept(s): y = x 2-2x - 3 Axis of Symmetry: a= b= c= Vertex: x y Y-Intercept:
17 Guided Practice for Example 1 1. Find the axis of symmetry and the vertex of the graph of the function y = x 2 2x 3. ANSWER x = 1, ( 1, 4)
18 Example 2 Guided Practice X-Intercept(s): y = 3x x - 1 Axis of Symmetry: a= b= c= Vertex: x y Y-Intercept:
19 Guided Practice for Examples 2 2. Graph the function y = 3x x 1. vertex and axis of symmetry. Label the
20 Storm Check (Think, Write, Discuss, Report) What is the standard form for a quadratic equation? The standard form for a quadratic equation is: Why are coefficients of a, b, and c important in graphing the quadratic equation? The coefficients of a, b, and c are important because.
21 Example 3 Find the minimum or maximum value Tell whether the function y = 3x 2 12x +10 has a minimum value or a maximum value. Then find the minimum or maximum value.
22 Example 3 Find the minimum or maximum value y = 3x 2 12x + 10 Tell whether the function has a minimum value or a maximum value. Then find the minimum or maximum value. SOLUTION Because a = 3 and 3 < 0, the parabola opens down and the function has a maximum value. To find the maximum value, find the vertex. b x = = 12 2a 2 ( 3) = 2 The x-coordinate is 2a b. 2 y = 3 ( 2) 12 ( 2) + 10 = 22 Substitute 2 for x. Then simplify. ANSWER The maximum value of the function is 22.
23 Storm Check (Think, Write, Discuss, Report) How can you tell if a parabola has a minimum or maximum value? You can tell if a parabola has a minimum value or maximum value by.
24 Vocabulary 1) Parabola ( y = ax 2 + bx + c ) 2) Axis of Symmetry x = -b 3) Vertex 2a 4) X-Intercept (Roots) (X,0) 5) Discriminant ( b 2-4ac )
25 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section TxtBk. Problems 3) Section Notes Copied on blank sheet of paper in Binder? Solved and Put in Binder? Table of Contents Date Description Date Due
26 Learning Target By the end of the period, I will graph quadratic equations in the standard form of y = ax 2 + bx + c. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.
27 Exit Ticket Out Exit Ticket Out X-Intercept(s): y = 2x 2-8x + 2 Axis of Symmetry: a= b= c= Vertex: x y Y-Intercept:
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