Presentation on theme: "Algebra II w/ trig 4.1 Quadratic Functions and Transformations"— Presentation transcript:
1Algebra II w/ trig 4.1 Quadratic Functions and Transformations 4.2 Standard Form of the Quadratic Function
2A 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.
3II.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) = -x²B. F(x) = 5x²C. F(x) = ¼x²
4III. 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)²-2The vertex is ( , )The axis of symmetry isSince a ____ 0, the parabola opens _____, and k = ___ is the ___________ value.Domain:__________ Range:_________
5IV. Graphing using vertex form. A. B. C. f(x) = -3 (x+2)² -1
6V. 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)