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# 1.1 anatomy of a quadratic function f2012

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### 1.1 anatomy of a quadratic function f2012

1. 1. 1. Anatomy of a Quadratic Function December 10, 2012 Unit 1. Quadratic Functions Review - Linear Functions y = mx + b Ax + By + C = 0 y = 3x - 1 y = -1x 4Unit 1 Quadratic Function
2. 2. 1. Anatomy of a Quadratic Function December 10, 2012 A quadratic function has a degree of 2 instead of 1. The function always has a x2 in the equation. ** Lets see what it looks like... **Quadratic - quadratum (Latin) - square f(x) = x2Unit 1 Quadratic Function
3. 3. 1. Anatomy of a Quadratic Function December 10, 2012 Anatomy of a parabola Vertex Anatomy of a parabola Axis of SymmetryUnit 1 Quadratic Function
4. 4. 1. Anatomy of a Quadratic Function December 10, 2012 Equations for quadratic functions The most common equation (and the one you need for drawing a parabola) is written in vertex form f(x) = a(x - p)2 + q The vertex can be found at (p, q) a, p, and q effect the graph in different ways. y = x2 is the basic graph f(x) = a(x - p)2 + q a makes the parabola wider or narrower. a>0 a<0 a≥1 a≤1Unit 1 Quadratic Function
5. 5. 1. Anatomy of a Quadratic Function December 10, 2012 f(x) = a(x - p)2 + q q causes a vertical translation. Easiest to tell when looking at the vertex f(x) = a(x - p)2 + q p causes a horizontal translation.Unit 1 Quadratic Function
6. 6. 1. Anatomy of a Quadratic Function December 10, 2012 E.g. Draw the parabola using the equation y = -3(x + 4) 2 + 1Unit 1 Quadratic Function
7. 7. 1. Anatomy of a Quadratic Function December 10, 2012 E.g. Draw the parabola: y = - 1/4(x - 4)2 + 1 Find the quadratic equation for the following:Unit 1 Quadratic Function
8. 8. 1. Anatomy of a Quadratic Function December 10, 2012 E.g. Draw the parabola: y = -(x - 3)2 + 9 Page 157: #3ab, 4a­dUnit 1 Quadratic Function
9. 9. 1. Anatomy of a Quadratic Function December 10, 2012 E.g. Determine the quadratic function in vertex form given the graphUnit 1 Quadratic Function