6.6 Finding the Vertex of a Parabola y = a(x – h) + k Vertex: (h, k)

6.6 Finding the Vertex of a Parabola Vertex: (h, k) In MT6, we have found… X Intercepts (also called zeros or roots): Y intercepts: AOS: Axis of Symmetry Now we look for the Vertex. The Vertex is the Highest or Lowest point in a parabola (also called Max and Min. The point on this parabola is a Min (Minimum)

6.6 Finding the Vertex of a Parabola We will learn two ways to find the Vertex of a parabola. They are… 1. Use completing the Square to find the Vertex form, and… 2. Use the Function language (input, output) to find the Vertex Let’s start with the Completing the Square Method We learned to complete the square in 5.8. If you need help, please refer to your notes. We will quickly step through the process. Here’s the first example… x 2 + 8x + 7 = 0 x 2 + 8x + ___ = -7 + ___ (x + ___) 2 = ___ 8 = Now turn it into Vertex Form: y = a(x – h) 2 + k Y = (x + 4) 2 - 9

6.6 Finding the Vertex of a Parabola Graphing Y = (x + 4) The vertex of your happy parabola (It’s positive) will be the zero of (x + 4) and -9. Therefore, the vertex is (-4, -9). Now graph… (-4, -9) That’s how you find the vertex using Complete the Square

6.6 Finding the Vertex of a Parabola You try this one… x 2 – 10x + 24 = 0 Step 1: Move 24 Now graph… Vertex: (5, -1) (5, -1) x 2 – 10x + ___ = ___ Step 2: Create Perfect Square (x - ___) 2 = ___ Why (x - ?) rather than (x + ?) Step 3: Place your numbers Step 4: Place in Vertex Form “y=“ y=(x - 5) Why did the “1” change signs? Why isn’t the vertex (-5, -1)?

6.6 Finding the Vertex of a Parabola f (x) = x 2 – 10x + 24 Awesome! You have learned how to find the vertex of a parabola using the Complete the Square method. Now for the function method: f (x) = Start with: Step 1: Find AOS Hint (-b/2a) A B C -(-10) = 10 = 5 x=5 is the AOS 2(1) 2 Step 2: Find f (5) f (5) = (5) 2 – 10(5) + 24 f (5) = 25 – = -1 Your vertex is your input and your output: Vertex: (5, -1) Notice you get the same answer whether you use Complete the Square method or the Function method. Please graph the same way.