Section 5.5 The Family of Quadratic Functions

Graph the following functions on the same set of axes Give the coordinates of the vertex for each graph

Graph the following functions on the same set of axes Give the coordinates of the vertex for each graph

The general form of a quadratic function with vertex (h, k) is The sign of a determines whether it opens up or down The magnitude of a determines how wide it is

To find the vertex of a general quadratic given by we use the vertex formula given by Definition: The axis of symmetry is a vertical line that divides the parabola into two symmetrical parts It is given by

Convert the following polynomials to the general form of a quadratic Given What is the vertex? Does it open up or down? How many x-intercepts does it have? Is it narrower or wider than y = x2? Convert the following polynomials to the general form of a quadratic

Do the following problems ALGEBRAICALLY If a ball is thrown up from a bridge and allowed to fall past the bridge to the ground, its height, h (in feet), after t seconds in the air is given by Do the following problems ALGEBRAICALLY How high is the bridge? What is the height of the ball When does the ball hit the ground? When does the ball return to the height from which it was thrown?