Warm Up Solve: Answer.

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Presentation transcript:

Warm Up Solve: Answer

Lesson 15 Quadratic Functions

Basic Quadratic Function Also known as Second Degree Function x y -4 -3 -2 -1 1 2 3 4 16 9 4 1 1 4 9 16

Quadratic Function - General form Parameters a, b & c change the graph of a function. Parameter “a” - graph on graphing calculator

Quadratic Function - General form Parameter “a” - graph on graphing calculator

Quadratic Function - General form Parameter "a" affects the opening of the parabola a > 1: narrows the opening a < 1: widens the opening + a (a > 0): the parabola is open upward - a (a < 0): the parabola is open downward

Quadratic Function - General form Parameter “b” - graph on graphing calculator Parameter "b" creates an oblique translation of the parabola (ie diagonal shift)

Quadratic Function - General form Parameter “c” - graph on graphing calculator Graph Parameter “c" is the initial value of the function (ie y-intercept)

Quadratic Function – Standard form Parameters a, h & k change the graph of a function. Parameter “a” - graph on graphing calculator Graph Parameter "a" affects the opening of the parabola

Quadratic Function – Standard form Parameter “h” - graph on graphing calculator Graph Parameter “h" shifts the graph horizontally (ie left and right)

Quadratic Function – Standard form Parameter “k” - graph on graphing calculator Graph Parameter “k" shifts the graph vertically (ie up and down)

Quadratic Function – Standard form If + a (a > 0), the parabola is open upward If - a (a < 0), the parabola is open downward The vertex of the parabola is: V (h, k) The parabola's axis of symmetry is the vertical line passing through the parabola's vertex. Its equation is : x = h Graph

Quadratic Function – Standard form Ex. Find the zero(s) of the following function: Algebraically - Zero(s)

Quadratic Function – Standard form Ex. Find the initial value of the following function: Algebraically - Init Val.

Quadratic Function – Standard form Finding the zero(s) of the Quadratic functions: Find the zero(s) of the following function:

Quadratic Function – Standard form Finding the zero(s) of the Quadratic functions: Case 1: There are two zeros Case 2: There is one zero Case 3: There are no zeros

Homework Workbook P. 89 #1, Activity 3, 4, 5 & 6 P. 94 #3 & 4