1. Algebra 2

3. Lesson 5-3 Graph y = (x + 1) 2 – 2. 2323 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). 2323 The graph of y = (x + 1) 2 – 2 is a translation of the graph of the parent function y = x 2. 2323 2323 You can graph it by translating the parent function or by finding the vertex and the axis of symmetry. 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 Additional Examples

4. Algebra 2 5-3 Example 1.Graph the function y = 4(x – 3) 2. 2.Identify the vertex and the y-intercept of the graph of y = –2(x + 5) 2 + 8. (–5, 8), –42

5. Algebra 2 Write the equation of the parabola shown below. Lesson 5-3 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 = 4aSimplify. = aSolve for a. 1212 The equation of the parabola is y = (x – 2) 2 – 5. 1212 Transforming Parabolas Additional Examples

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

7. Algebra 2 5-3 Example 3.Write the equation y = 3x 2 + 12x – 1 in vertex form. y = 3(x + 2) 2 – 13