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4.2 standard form of a quadratic function (Part 1)

Standard form of a quadratic function is f(x) = ax^2 + bx + c. The graph is a parabola that opens up if a > 0 and opens down if a < 0. The axis of symmetry is the line x = -b/2a and the vertex is (-b/2a, f(-b/2a)). To graph in standard form, identify a, b, c, find the axis of symmetry and vertex, then plot the y-intercept and use reflection to sketch the parabola. The document provides an example of using standard form to identify the vertex, axis of symmetry, minimum/maximum value, and range of a parabola.

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4.2 STANDARD FORM OF A QUADRATIC FUNCTION Part 1: Properties of Standard Form and Graphing using Standard Form
QUADRATIC FUNCTIONS  Vertex Form:  Standard Form is another way to write the equation of a quadratic function. Standard form is: Both forms can represent the same function. Vertex form makes it easy to identify the vertex and other information about the graph. Standard form is easier to put into a graphing calculator and is more “formal”.
PROPERTIES OF STANDARD FORM  The graph of is a parabola.  If a > 0, the graph opens up. If a < 0, the graph opens down.  The axis of symmetry is the line  The x – value of the vertex is and the y – value of the vertex is  The y – intercept is (0, c)
EXAMPLE: IDENTIFY THE VERTEX, AXIS OF SYMMETRY, THE MAXIMUM OR MINIMUM VALUE, AND THE RANGE OF THE PARABOLA
EXAMPLE: IDENTIFY THE VERTEX, AXIS OF SYMMETRY, THE MAXIMUM OR MINIMUM VALUE, AND THE RANGE OF THE PARABOLA
GRAPHING A FUNCTION IN STANDARD FORM 1. Identify a, b, and c 2. Identify and sketch the axis of symmetry, 3. Identify and plot the vertex, 4. Identify and plot the y – intercept, (0, c) 5. Use the axis of symmetry and y – intercept to plot the reflected point 6. Sketch the parabola
GRAPH EACH FUNCTION
GRAPH EACH FUNCTION