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Pre-Calculus with Mrs. Pfrommer

Pre-Calculus with Mrs. Pfrommer. Reminder: Take out pencil, HW on the left corner of your desk, start the Do Now. Homework: graphing worksheet #4. Objectives: Students will identify the form of a given quadratic equation Students will be able to graph a quadratic given in vertex form

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Pre-Calculus with Mrs. Pfrommer

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  1. Pre-Calculus with Mrs. Pfrommer Reminder: Take outpencil, HW on the left corner of your desk, start the Do Now. Homework: graphing worksheet #4 • Objectives: • Students will identify the form of a given quadratic equation • Students will be able to graph a quadratic given in vertex form • Students will be able to write an equation in vertex form given a graph Do Now: Simplify: 1) -2(x – 4)2 + 6 2) 3x4 + 6x2 – 18 – 2x2 (x2 + 4) Agenda: • Do Now • Vertex Form • Graphing quadratics given vertex form • Writing equations given graphs

  2. Quadratic Equation Forms • There are 3 forms of a quadratic equation: • Standard Form f(x) = ax2 + bx + c • Factored f(x) = a(x – r1)(x – r2) • Vertex Form: f(x) = a(x – h)2 + k • Factored form gives you x-intercepts, y-intercept with a little bit of work, and you can find the vertex pretty easily • Standard form gives you the scale factor, concavity and the y-intercept • Vertex form gives you the vertex (h,k), the scale factor, concavity and the y-intercept.

  3. Graphing using Vertex Form Graph y = (x+2)2 – 3 Step 1: name the vertex (-2,-3) Step 2: Find the y-intercept Step 3: Use parabola’s symmetry to find another point (-4, 1)

  4. Try: f(x) = -2(x+1)2 + 4 You should get: Vertex (-1,4) Y-intercept: (0,2) Other point (-2,2)

  5. Do # 5 & 6 on HW packet • #5) vertex (2, 3) y-intercept (0,7) opens up • #6) vertex (-5, -3) y-intercept (0,22) opens up

  6. Graph  Equation Write an equation for this graph: Step 1: Identify critical points  vertex and y intercept Step 2: plug the vertex into the vertex equation form: y = a(x-h)2 + k Step 3: find scale factor by plugging y-intercept into the equation You get: y= 2(x+1)2 - 5

  7. Now try # 1 on graph  equation sheet • Vertex (3, -2) and the y-intercept is (0, ?) but there are 2 other points (5, 6) or (1,6) that you can use for finding the scale factor a. So, the equation is: y = 2(x – 3)2 - 2

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