1. Bellringer
Find the equation of the parabola given the following points, then find the axis of symmetry and the minimum value. (-3,-2), (-4,1), (0,1)

2. 5-3 Transforming Parabolas

3. Objectives
Using Vertex Form

4. Vocabulary Vertex Form of a Quadratic Equation y = a(x - h)² + k
The Family of Quadratic Functions
Parent Function: y = x²
Reflection in the x-axis: y = -x²

5. Vocabulary y = a(x + h)² + k Stretch: a > 1 Shrink: 0 <a < 1
Graph shifts up: k > 0
Graph shifts down: k < 0
Graph shifts right: h < 0
Graph shifts left: h > 0
The vertex is (h, k) and the axis of symmetry is the line x = h

6. Using the Vertex Form to Graph a Parabola
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
You can graph it by translating the parent function or by finding the vertex and the axis of symmetry.
Step 1: Graph the vertex (–1, –2). Draw the axis of symmetry x = –1.
Step 4: Sketch the curve.
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 2: Find another point. When x = 2,
y = (2 + 1)2 – 2 = 4. Graph (2, 4). 2 3

7. Whiteboards y = 4(x - 2) y = (x - 2) – 3 y = (x - 6) + 6

8. Writing the Equation of the Parabola
Write the equation of the parabola shown below.
y = a(x – h)2 + k Use the vertex form.
y = a(x – 2)2 – 5 Substitute h = 2 and k = –5.
–3 = a(0 – 2)2 – 5 Substitute (0, –3).
2 = 4a Simplify.
= a Solve for a. 1 2
The equation of the parabola is y = (x – 2)2 – 5. 1 2

9. Whiteboards

10. Real World Example
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) 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?
Start by drawing a diagram.
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.

11. Continued (continued) To find the wall’s height, find y for x = 0.
= 15
The wall is 50 ft long and 15 ft high.

12. Converting to Vertex Form
Write y = –7x2 – 70x – 169 in vertex form. b 2a
x = –
= –
(–70)
2(–7)
= –5
Find the x-coordinate of the vertex.
Substitute for a and b.
y = –7 (–5)2 – 70(–5) – 169
= 6
Find the y-coordinate of the vertex.
The vertex is at (–5, 6).
= –7(x – (–5))2 + 6
y = a(x – h)2 + k
Write in vertex form.
Substitute for a, h and k.
= –7(x + 5)2 + 6
The vertex form of the function is y = –7(x + 5)2 + 6.

13. Whiteboards
Write in vertex form.

14. Homework
5-3 Pg # 1, 2, 13, 14, 27, 28