G8 S1 Project Week PPT (Exponential Graphs)

Linear, Quadratic and Exponential Graphs

Lesson Objectives

By reading key features of exponential graphs and watching videos, learn about this new graph.

New Graph: Exponential Graph

By reading key features of Linear and Quadratic Graphs, refresh your memories on these graphs.

Review Linear and Quadratic Graphs

y = mx + c is the general equation for a straight-line graph.
‘m’ is equal to the gradient of the graph.
‘c’ is the value where the line crosses the y-axis and is called the y-intercept.

Linear Graphs

y = ax² + bx + c is the general equation for a quadratic graph
Axis of Symmetry
Vertex
Y-intercept
X-intercepts (Roots)

Quadratic Graphs

f(x) = a

Exponential Graphs

​x

​x

​x

Exponential Functions

An exponential function is one in which the input occurs as a power. It is written in the form:

​Let’s take a look at the graph of y = ax for integer values of a from 2 to 5 inclusive.

​The larger the value of a, the steeper the graph, but all take the same basic shape.

​Now, we’ll consider what happens when a is less than 1, but greater than 0.

​As before, the graph intersects the y-axis at 1. However, compared to functions where a > 1, the shape of the graph has been reflected in the y-axis.

As x decreases below 0, the output increases, and very small, negative x values give us large outputs.

As x increases above 0, the output again tends towards 0 and the asymptote at y = 0 remains.

This time, the smaller the value of a, the steeper the graphs, but when 0 < a < 1, our gradients are always negative – the function is purely decreasing.

Learn more from videos

​https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:graphs-of-exponential-growth/v/graphing-exponential-functions

Connect algebra to real life in this Graphing Linear, Exponential and Quadratic Functions Regression Project.

This project based learning activity is perfect for students to write a linear, quadratic, or exponential equation, graph the scatter plot and function, and analyze the data.

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Real Life Application