CCGPS Geometry Day 39 (3-5-15) 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

Daily Check Give the transformations for each of the following functions? f(x) = (x - 2)2 + 4 f(x) = -3x2 f(x) = ½ (x+3)2 Write the equation in vertex form for the following graph.

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

Writing in Standard Form Multiply out each of the following functions. y = (x – 1)2 + 8 y = 2(x + 3)2 – 5 y = -(x – 4)2 + 3 y = 2(x + 1)2 – 2 This is how you convert from vertex form to standard form.

Converting from standard to vertex form: Find the AXIS of SYMMETRY : Find VERTEX (h, k) h = x k is found by substituting “x” “a” – value for vertex form should be the same coefficient of x2 in standard form. Check by using another point (intercept)

Example Given f(x) = x2 + 8x + 10 1) 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.

Write in vertex form. Find vertex and axis of symmetry. PRACTICE METHOD #2: Write in vertex form. Find vertex and axis of symmetry. [5] [6]

Write in vertex form. Find vertex and axis of symmetry. PRACTICE METHOD #2: Write in vertex form. Find vertex and axis of symmetry. [7] [8]