4.1 Quadratic Functions and Transformations Learning Goal identify and graph quadratic functions

Vocabulary parabola : the graph of a quadratic function vertex : minimum or maximum value; where the parabola intersects the axis of symmetry axis of symmetry : a line that divides the parabola into 2 parts, mirror images

Finding the vertex of a parabola equation vertex vertex form

Translating a parabola vertex form : the graph of translated h units horizontally and k units vertically h k positive right up negative left down vertex: axis of symmetry:

Ex 1 Graph each function. How is each graph a translation of ?

Reflecting a parabola vertex form : the graph of reflected in the x-axis value of a direction of opening min/max value range graph positive up minimum negative down maximum

Ex 2 Determine the direction of opening for each quadratic function. Determine if the function has a minimum or maximum and state its value.

Stretching or compressing a parabola compression 0 < a < 1

Ex 3 Determine if each quadratic function is stretched or compressed.

Ex 3 Graph. Find the vertex, axis of symmetry, y-intercept, maximum or minimum, the domain and range. vertex aos y-intercept SP max/min domain range

Ex 4 Graph. Find the vertex, axis of symmetry, y-intercept, maximum or minimum, the domain and range. vertex aos y-intercept SP max/min domain range

Writing the equation of a parabola Ex 4 Write an equation of the quadratic function in vertex form with

EX 5 Write the equation in vertex form of the given parabola. Convert your answer to standard form.

Ex 6 Write a quadratic function in vertex form that models the path of the dolphin’s jump.