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Transforming Parabolas

2 3. Graph y = ( x + 1) 2 – 2. 2 3. The graph of y = ( x + 1) 2 – 2 is a translation of the graph of the parent function y = x 2. 2 3. Step 1: Graph the vertex (–1, –2). Draw the axis of symmetry x = –1. Step 2: Find another point. When x = 2,

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Transforming Parabolas

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  1. 2 3 Graph y = (x + 1)2 – 2. 2 3 The graph of y = (x + 1)2 – 2 is a translation of the graph of the parent function y = x2. 2 3 Step 1: Graph the vertex (–1, –2). Draw the axis of symmetry x = –1. Step 2: Find another point. When x = 2, y = (2 + 1)2 – 2 = 4. Graph (2, 4). 2 3 Step 3: Graph the point corresponding to (2, 4). It is three units to the left of the axis of symmetry at (–4, 4). Step 4: Sketch the curve. Transforming Parabolas Lesson 5-3 Additional Examples You can graph it by translating the parent function or by finding the vertex and the axis of symmetry.

  2. 1 2 = a Solve for a. 1 2 The equation of the parabola is y = (x – 2)2 – 5. Transforming Parabolas Lesson 5-3 Additional Examples Write the equation of the parabola shown below. y = a(x – h)2 + kUse the vertex form. y = a(x – 2)2–5Substitute h = 2 and k = –5. –3 = a(0 – 2)2 – 5Substitute (0, –3). 2 = 4a Simplify.

  3. Start by drawing a diagram. Transforming Parabolas Lesson 5-3 Additional Examples A long strip of colored paper is attached as a party decoration at exactly opposite corners of the back wall of a rectangular party room. The strip approximates a parabola with equation y = 0.008(x – 25)2 + 10. The bottom left corner of the back wall is the origin and x and y are measured in feet. How far apart are the side walls? How high are they? The function is in vertex form. Since h = 25 and k = 10, the vertex is at (25, 10). The vertex is halfway between the two corners of the wall, so the width of the wall is 2(25 ft) = 50 ft.

  4. y = 0.008 (0 – 25)2 + 10 y = 0.008 (–25)2 + 10 = 15 Transforming Parabolas Lesson 5-3 Additional Examples (continued) To find the wall’s height, find y for x = 0. The wall is 50 ft long and 15 ft high.

  5. b 2a x = – Find the x-coordinate of the vertex. Substitute for a and b. (–70) 2(–7) = – = –5 y = –7 (–5)2 – 70(–5) – 169 Find the y-coordinate of the vertex. = 6 y = a(x – h)2 + k Write in vertex form. = –7(x – (–5))2 + 6 Substitute for a, h and k. = –7(x + 5)2 + 6 Transforming Parabolas Lesson 5-3 Additional Examples Write y = –7x2 – 70x – 169 in vertex form. The vertex is at (–5, 6). The vertex form of the function is y = –7(x + 5)2 + 6.

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