Graph y = -5x2 – 2x + 3 and find the following: Warm Up Graph y = -5x2 – 2x + 3 and find the following: Vertex Axis of Symmetry Y-intercept X-intercept

HW Check 5.1

Section 5.3 - Translating Parabolas

Standard form vertex

Find the vertex of y = x2 – 4x + 6

Vertex Form Graph the following functions. Identify the vertex of each. 1. y = (x – 2)2 2. y = (x + 3)2 – 1 3. y = -3(x + 2)2 + 4 4. y = 2(x + 3)2 + 1

Vertex of Vertex Form The Vertex form of a quadratic equation is a translation of the parent function y = x2

Vertex of Vertex Form

Identifying the Translation Given the following functions, identify the vertex and the translation from y = x2 y = (x + 4)2 + 7 y = -(x – 3)2 + 1 y = ½ (x + 1)2 y = 3(x – 2)2 – 2

Writing a Quadratic Equations

Try one! Write an equations for the following parabola.

One More! Write an equation in vertex form: Vertex (1,2) and y – intercept of 6

Converting from Standard to Vertex form Things needed: Find Vertex using x = -b/2a, and y = f(-b/2a) or by graphing in the calculator. This is your (h, k). Then use the the a from standard form.

Example Convert from standard form to vertex form. y = -3x2 + 12x + 5

Example Convert from standard form to vertex form. y = x2 + 2x + 5

Try Some! Convert each quadratic from standard to vertex form. y = x2 + 6x – 5 y = 3x2 – 12x + 7 y = -2x2 + 4x – 3

Word Problems A ball is thrown in the air. The path of the ball is represented by the equation h = -t2 + 8t. What does the vertex represent? What does the x-intercept represent?

Word Problems A lighting fixture manufacturer has daily production costs of C = .25n2 – 10n + 800, where C is the total daily cost in dollars and n is the number of light fixture produced. How many fixtures should be produced to yield minimum cost.