2.1 Quadraticsnts.notebook. September 10, 2018

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2 A quadratic function is a polynomial function of second degree. The graph of a quadratic function is called a parabola. 2

3 Standard Form: Intercept Form: Vertex Form: f(x) = a(x h) 2 + k vertex: (h, k) y k = a(x h) 2 Another way to write it! Name the vertex. Does it open up or down? Does have a vertical shrink or stretch? 3

4 Minimum opens upward leading coefficient positive Maximum opens downward leading coefficient negative (vertex) 4

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8 Sketch the graph of the quadratic function. Identify the vertex and x intercepts. f(x) = x 2 9 8

9 Sketch the graph of the quadratic function. Identify the vertex and x intercepts. f(x) = (x 6)

10 Write the vertex form of the quadratic that has vertex (1, 2) and passes through (3, 6). y = a (x h) 2 + k 10

11 Write the vertex form of the graphed function. y = a (x h) 2 + k 11

12 Write the equation in the form: of the graphed function. 12

13 Write the vertex form of the graphed function. 13

14 Write the vertex form of the graphed function. 14

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16 To Find Vertex: 1. y k = a (x h) 2 and vertex is (h, k). 2. When equation is in standard form f(x) = Ax 2 + Bx + C, x = then substitute that number to get the y value. 3. For an estimate, put in calculator and find maximum or minimum. Does not give exact value, only approximation. 4. In intercept form,, then substitute the x in to the original equation and solve for y. 16

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19 To Find x intercept: 1. Set equation equal to zero and solve for x. (When equation = 0 that means y = 0 which is what an x intercept is). factor and solve quadratic formula 2. For an estimate, put in calculator and find zero by pressing 2nd calc then zero. Does not give exact value, only approximation. 19

20 Sketch the graph of the quadratic function. Identify the vertex and x intercepts. "Identify the vertex" = write in standard form "x intercepts"... set f(x) = 0 f(x) = x 2 + 2x 8 20

21 Sketch the graph of the quadratic function. Identify the vertex and x intercepts. Put in vertex form. f(x) = 2x 2 + 8x

22 Factor the following: x 2 8x x x + 9 Using Complete the Square, write in vertex form and state the vertex y = 2x 2 + 4x 4 y = 4x x

23 Sketch the graph of the quadratic function. Identify the vertex and x intercepts. Write in standard form. 23

24 Word problems... typical questions... initial height, maximum height, when does it hit the ground? 24

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26 With your partner, answer the following 2 questions. You will be handing this in, so answer everything thoroughly. If you have your book, please go to pg and 67 26

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29 Sketch the graph of the quadratic function. Identify the vertex and x intercepts. Write in vertex form. f(x) = x 2 + 3x + 1/4 29

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31 Let's start #61 together a. What does it look like? b. Radius of a semicircular ends of track r = 1/2y distance around 2 semicircular parts of a track. d = 2πr = 2π(1/2)y = πy c. Distance traveled around the track in one lap: d = πy + 2x = 200 solve for y d. Area of rectangular region: A = xy = x ( 200 2x) Complete the square and write answer in vertex form 2/π (x 50) /π e. The area is the maximum when x = 50 and y = 100/ π 31

32 62. 4x + 3y = 200 skip b, and e! Use the calculator to find the max in c. 32

33 Never use to replace homework, only to help guide you! 33