ESSENTIAL UNDERSTANDING ANDOBJECTIVES Essential Understanding: Standard Form: to find zeros of a quadratic function y = ax2 + bx + c, solve the related quadratic equation = ax2 + bx + c Objectives: Students will be able to: Solve quadratic equations by factoring Solve quadratic equations by graphing
IOWA CORE CURRICULUM Algebra A.SSE.1a. Interpret parts of an expressions, such as terms, factors, and coefficients A.APR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (concept byte)
ZERO What do you think when I say the zero of a function? Zero of a function is where the graph crosses the x- axis. You can solve quadratic equations in standard form by factoring, using the zero product property Zero product property: if ab = 0, then a = 0 or b = 0
EXAMPLE Solving a Quadratic Equation by Factoring What is the solution to: x2 – 7x +12 = 0 x2 + 3x -18 = 0
EXAMPLE Solving by Graphing What is the solution to: 4x2 – 14x + 7 = 4 – x x2 +2x = 24
The function y = -0.03x2 + 1.6x models the path of a kicked soccer ball. The height is y, the distance is x, and the units are in meters. How far does the soccer ball travel? How high does the soccer ball go? Describe a reasonable domain and range for the function.