# Algebra II w/ trig 4.1 Quadratic Functions and Transformations

## Presentation on theme: "Algebra II w/ trig 4.1 Quadratic Functions and Transformations"— Presentation transcript:

Algebra II w/ trig 4.1 Quadratic Functions and Transformations
4.2 Standard Form of the Quadratic Function

A parabola is the graph of a quadratic function, which you can write in the form f(x) = ax² + bx + c, where a å 0. The vertex form of the quadratic is f(x) = a(x-h)2+k, where a å 0. The axis of symmetry is a line that divides the parabola into two mirror images. The equation of the axis of symmetry is x = h. The vertex of the parabola is (h, k), the intersection of the parabola and its axis of symmetry.

II.The parent quadratic function is f(x) = x². Its graph is a parabola. What is its axis of symmetry? Vertex? Graph and describe. F(x) = -x² B. F(x) = 5x² C. F(x) = ¼x²

III. The vertex form, f(x) = a(x-h)² + k , gives you information about the graph of f without drawing the graph. If a>0, k is the minimum value of the function. If a<0, K is the maximum value of the function. Y = 3(x-4)²-2 The vertex is ( , ) The axis of symmetry is Since a ____ 0, the parabola opens _____, and k = ___ is the ___________ value. Domain:__________ Range:_________

IV. Graphing using vertex form. A. B.
C. f(x) = -3 (x+2)² -1

V. Write the equation of the parabola with the given info. A
V. Write the equation of the parabola with the given info. A. Vertex (2, 3) AND (0,1) B. Vertex (1,3) and (-2, -15)

VI. Given the parabola, write the equation.

Pre-Ap Homework P. 199 # 7-51odd, and 55