Algebra II Quarter 2: Handout #6 Name ________________________ Date _____________ Period _____ 5.1 Graphing Quadratic Functions Notes A quadratic function has the standard form y = ax2 + bx + c, where a ≠ 0. The graph of a quadratic function is a parabola (“U-Shaped”). The lowest (minimum) or highest (maximum) point on a parabola is called the vertex. The axis of symmetry for a parabola is the vertical line going through the vertex. How to graph a quadratic function in standard form, y = ax2 + bx + c: o The parabola opens up if a > 0 and has a minimum. o The parabola opens down if a < 0 and has a maximum. o If |a| > 1, then the parabola become more narrow. (Opposite of intuition.) o If |a| < 1, then the parabola becomes wider. (Opposite of intuition.) −b o The x-coordinate for the vertex can be found using the formula: 2a o Once you have the x-coordinate for the vertex, substitute it back into the given equation and solve for the y-coordinate. o Axis of symmetry is the vertical line: x = −b 2a How to graph a quadratic function in Vertex form, y = a(x – h)2 + k: o Vertex is (h, k) o Axis of symmetry is x = h o The parabola opens up if a > 0 and has a minimum. o The parabola opens down if a < 0 and has a maximum. o If |a| > 1, then the parabola become more narrow. (Opposite of intuition.) o If |a| < 1, then the parabola becomes wider. (Opposite of intuition.) Algebra II Quarter 2: Handout #6 Examples 1. Write the quadratic function in standard form: a. y = –(x + 4)(x – 9) b. y = 3(x – 1)2 + 8 Algebra II Quarter 2: Handout #6 2. Graph the quadratic functions: a. y = x2 – 8x + 6 i. Graph characteristics: 1. Vertex: _________________________ 2. Axis of Symmetry: ____________________ 3. Open up or down?: ______________________ 4. Narrow, Wide, Normal?: ______________________ Algebra II Quarter 2: Handout #6 b. –(x + 2)(x – 4) i. Graph characteristics: 1. Vertex: _________________________ 2. Axis of Symmetry: ____________________ 3. Open up or down?: ______________________ 4. Narrow, Wide, Normal?: ______________________ Algebra II Quarter 2: Handout #6 c. y = 4(x – 1)2 + 5 i. Graph characteristics: 1. Vertex: _________________________ 2. Axis of Symmetry: ____________________ 3. Open up or down?: ______________________ 4. Narrow, Wide, Normal?: ______________________

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# 5.1 Graphing Quadratic Functions Notes