3.3 Quadratic Functions Quadratic Function: 2nd degree polynomial

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Presentation transcript:

3.3 Quadratic Functions Quadratic Function: 2nd degree polynomial Graph is a parabola Vertex (max or min) Opens up or down Has exactly one y-intercept Can have 0, 1, or 2 x-intercepts

Axis of Symmetry: Vertical line through the vertex (h, k) that cuts the parabola in half. A.S. x = h

Vertex Form: f(x) = a(x – h)2 + k (Transformation) vertex = (h, k) Ex. 1 Find the vertex and the axis of symmetry of this quadratic. f(x) = -2(x – 3)2 – 7

Standard form: f(x) = ax2 + bx + c (polynomial) vertex = ( ) Ex. 2 Find the vertex of y = x2 – 2x + 3

To find the x-intercepts, let y = 0. To find the y-intercept, let x = 0. If +a, then parabola opens up. If –a, then parabola opens down.

Find the vertex, axis of symmetry, & determine if the parabola opens up or down. 3a. g(x) = -6(x –2)2 – 5 Vertex: A.S.: Up or Down 3b. f(x) = 4(x +1)2 + 3 Vertex: A.S.: Up or Down

Find the x & y intercepts of each parabola 4a. f(x) = x2 + 8x – 1 y-int: (x = 0) x-int: (y = 0) 4b. h(x) = -2(x+3)(x+1) y-int: x-int:

Write each equation in standard (polynomial) form. y = ax2 + bx + c 5a. g(x) = 2(x- 1)(x + 6) 5b. f(x) = 2(x + 3)2 - 4

Write the following functions in transformation (vertex) form Write the following functions in transformation (vertex) form. f(x) = a(x – h)2 + k 6a. x2 + 4x – 5 = f(x) 6b. -(x – 4)(x+ 2) = f(x)