Pre-Calculus 11 Workbook - McGraw-Hill Ryerson

3.2 Investigating Quadratic Functions in Standard FormKEY IDEAS• The standard form of a quadratic function is f (x) = ax 2 + bx + c or y = ax 2 + bx + c,where a ≠ 0.• The graph of a quadratic function is a parabola that– is symmetric about a vertical line, called the axis of symmetry, that passes through thevertex– opens upward and has a minimum value if a > 0– opens downward and has a maximum value if a < 0– has a y-intercept at (0, c) that has a value of c• You can determine the vertex, domain and range, direction of opening, axis of symmetry,x-intercepts, y-intercept, and maximum or minimum value from the graph of a quadraticfunction.vertexymaximumvalueyaxis ofsymmetryx-interceptpx- intercept0xaxis ofsymmetryy-interceptx-intercept 0y-interceptminimum valuepvertexx-interceptxDomain: all real numbersRange: all real numbers lessthan or equal to themaximum value of yDomain: all real numbersRange: all real numbers greaterthan or equal to theminimum value of y• For any quadratic function in standard form, the x-coordinate of the vertex is given by__x = – b2a.& See page 166 of Pre-Calculus 11 for how the formula for x-coordinate of the vertexwas derived.12 MHR • Chapter 3 978-0-07-073882-9