Daily Check Give the transformations for each of the following functions? 1)f(x) = (x - 2) )f(x) = -3x 2 3)f(x) = ½ (x+3) 2 Write the equation in vertex form for the following graph.

Warm-up Multiply out each of the following functions. 1)y = (x – 1) )y = 2(x + 3) 2 – 5 3)y = -(x – 4) )y = 2(x + 1) 2 – 2 This is how you convert from vertex form to standard form.

CCGPS Geometry Day 39 ( ) UNIT QUESTION: How are real life scenarios represented by quadratic functions? Today’s Question: How do we change from standard form to vertex form of a quadratic? Standard: MCC9-12.A.SSE.3b, F.IF.8

Summary of Day One Findings Parabolas Vertex Form Vertex: (h, k) Axis: x = h Rate: a (+ up; – down)

What's the pattern? (x + 6) x6 x 6 x2x2 6x6x 6x6x36 x x + 36 How about these? x 2 + 4x ______(x _____ ) 2 x x ______(x _____ ) 2 x 2 – 14x ______(x _____ ) – 7 COMPLETING THE SQUARE

Converting from standard form to vertex form can be easy… x 2 + 6x + 9 (x + 3) 2 x 2 – 2x + 1 = x 2 + 8x + 16 = x x = (x – 1) 2 (x + 4) 2 (x + 10) 2 … but we're not always so lucky COMPLETING THE SQUARE

The following equation requires a bit of work to get it into vertex form. y = x 2 + 8x + 10 y = (x 2 + 8x ) – is added to complete the square. 16 is sub- tracted to maintain the balance of the equation. y = (x + 4) 2 – 6 The vertex of this parabola is located at ( – 4, – 6 ). COMPLETING THE SQUARE

Lets do another. This time the x 2 term is negative. y = – x x – 5 y = – (x 2 – 12x ) – The 36 in parentheses becomes negative so we must add 36 to keep the equation balanced. y = – (x – 6) The vertex of this parabola is located at ( 6, 31 ). y = – (x 2 – 12x ) – 5 Un-distribute a negative so that when can complete the square y = ( – x x ) – 5 COMPLETING THE SQUARE

Find the value to add to the trinomial to create a perfect square trinomial : (Half of “b”) 2 [A] [B] [C][D]

Example 1Type 1: a = 1 Write in vertex form. Identify the vertex and axis of symmetry. [A] [B]

Write in standard form. Identify the vertex and axis of symmetry. [A] [B] Example 2Type 1: a≠1

Method #2: SHORTCUT 1.Find the AXIS of SYMMETRY : 2.Find VERTEX (h, k) h = x k is found by substituting “x” 3.“a” – value for vertex form should be the same coefficient of x 2 in standard form. Check by using another point (intercept)

Method #2 Example Given f(x) = x 2 + 8x ) Find a, b, and c. 2) Find the line of symmetry or “h” using x = -b/2a 3) Find the y value of the vertex, or “k” by substituting “x” into the equation. So, the vertex is at (-4, 6). 4) Write the equation in vertex form using the “h” and “k” found. “a” will be the same thing as in Step 1.

[1] PRACTICE METHOD #2: Write in vertex form. Find vertex and axis of symmetry. [2]

[3] PRACTICE METHOD #2: Write in vertex form. Find vertex and axis of symmetry. [4]