Lesson 8-3 Graphing Quadratic Functions Lesson 8-4 Transforming Quadratic Functions Obj: The student will be able to 1) Graph a quadratic function in the form y = ax² + bx + c 2) Graph and transform quadratic functions HWK: Worksheet

What is the y-intercept What is the y-intercept? What is the x-coordinate of the point of the y-intercept? Using y = ax² + bx + c, what is the value of y at the y-intercept?

Steps to graph Quadratic Functions Step 1: Find the axis of symmetry Step 2: Find the vertex Step 3: Find the y-intercept Step 4: Find two or more points on the same side of the axis of symmetry as the point containing the y-intercept Step 5: Graph the axis of symmetry, vertex, point containing the y-intercept and two other points Step 6: Reflect the points across the axis of symmetry and connect points with a smooth curve

Graph each quadratic function Ex 1) y = 2x² + 6x + 2

Ex 2) The height in feet of a football that is kicked can be modeled by the function f(x) = -16x² + 64x where x is the time in seconds after it is kicked. Find the football’s maximum height and the time it takes the football to reach this height. Then find how long the football is in the air.

Quadratic parent function is y = x². All others are transformations. y = x² or f(x) = x² Axis of symmetry Vertex Zeroes of the function

Compare f(x) = x² g(x) = 1 2 x² h(x) = -3x² What is the same? What is different?

Width of a Parabola The graph of f(x) = ax² is narrower than the graph of f(x) = x² if │a│ > 1 and wider if │a│ < 1

Order the functions from narrowest graph to widest graph Ex 1) f(x) = -x² and g(x) = 2 3 x² Ex 2) f(x) = -4x² and g(x) = 6x² and h(x) = 0.2x²

Compare f(x) = x² g(x) = x² = 4 h(x) = x² + 3 What is the same? What is different?

Vertical Translations of a Parabola The graph of the function f(x) = x² + c is the graph of f(x) = x² translated vertically If c > 0 the graph of f(x) = x² is translated c units up If c < 0 the graph of f(x) = x² is translated c units down

Compare the graph of each function with the graph of f(x) = x² Ex 3) g(x) = -x² - 4 Ex 4) g(x) = 3x² + 9

Ex 5) g(x) = 1 2 x² + 2

Write the two height functions and compare their graphs. Ex 6) The quadratic function h(t) = -16t² + c can be used to approximate the height h in feet above the ground of a falling object t seconds after it is dropped form a height of c feet. Two different water balloons are dropped from different heights. Roy dropped his balloon from 64 ft and Sally dropped hers from 144 ft. Write the two height functions and compare their graphs. Use the function to tell when each water balloon reaches the ground