By Adam Kershner and Fred Chung

Key points Slope Intercept Supply and demand

Linear function is F(x) = mx + B M stands for the slope. The slope is the average rate of change. B is the Y intercept

How to find the slope of a linear function To find the slope of a linear function you need to calculate the change in Y over the change in X. Or using the formula: Y 2 – Y 1 X 2 – X 1 The slope is increasing if m is positive. The slope is decreasing if m is negative. The slope is constant if the slope is zero. Y = 4X + 10 The slope in this problem is positive

Point Slope Form y – y 1 = m( x – x 1 ) Y - CordinateX - CordinateSlope

Recommended Problems for 3.1 are: 13, 18, 19,23, 24, 27, 32, 41, and 47

3.2 Building Linear Functions from Data How to Graph Line of Best Fit

Scatter Plots (X, Y) Moves left and right Moves up and down A scatter plot is linear when the dots are close to each other. A scatter plot is nonlinear if the dots are more spread out.

How to find Line of best fit You can either use a calculator or do it by hand. With a calculator you use the LINear REGression command. When you find the line of best fit by hand you find the slope between two points that are on opposite sides of the points.

Recommended Problems for 3.2 are: 3, 7, 9, 14, 21

3.3 Quadratic Functions and Their Properties Shape of Parabola Graph by Steps Graph by Transformations Finding Mins and Max

Quadratic Functions F(x) = ax 2 + bx + c A quadratic Function is in the shape of a parabola If a is positive then it opens up If a is negative then it opens down

Graphing by Steps When a gets bigger the graph becomes narrower when it gets smaller the graph becomes wider. The X coordinate of the vertex is found by using the formula: -b 2a To find the Y coordinate you substitute the x value into the function To find the y intercept put in 0 for x To find the x coordinates use the quadratic formula Put all these parts together on a graph and connect the lines Pg. 141

Graphing by Transformations First you need to complete the square forming a function that looks like: 2(X + 2) Causes a vertical stretch Shifts two units left Shifts 3 units down Pg. 141

Finding Min and Max If a < 0 then the Max is found by using: -b 2a If a > 0 then the Min is found by using: -b 2a

Recommended Problems for 3.3 are: 18, 21, 27, 44, 47, 57, 59, 64

3.4 Quadratic Models; Building Quadratic Functions from data Maximizing Revenue Analyzing the Motion of a Projectile Linear Regression on a calculator

Maximizing Revenue This formula is for calculating revenue: R = px R = revenue p= price x = number of units sold Analyzing the Motion of a Projectile Height of the projectile after X amount of time is: h (x) = -32x 2 + X + H I VI2 V I = Initial velocity H I = Initial Height Linear Regression on a calculator To calculate linear regression on a calculator you must first input the data, then using the QUADratic REGression button obtain the results. This will give you a, b, and c but you must plug them into the quadratic formula for the full answer

Recommended Problems for 3.4 are: 6, 7, 12, 28,29

3.5 Inequalities Involving Quadratic Functions Graphing Inequalities Solution Set

Graphing a quadratic inequality is the same as graphing a regular quadratic function except for that when graphing a quadratic inequality you need to have a solution set The solution set is calculated by either using the x – intercepts if the graph is below the x – axis or points on the line g (x) (if the inequality we are solving is f(x) Solution Set

Recommended Problems for 3.5 are: 6, 13, 20, 21, 26, 32