Mr. Santos wants to enclose the rectangular parking lot beside his house by putting a wire fence on the three sides as shown in the picture. If the total length of the wire is 80 m, find the dimensions of the parking lot that will enclose a maximum area.

1. In the picture above, if we let w be the length and l  be the length, what is the expression for the sum of the measures of the three sides of the parking lot?

2. What is the length of the rectangle in terms of the width?

3. Express the area (A) of the parking lot in terms of the width.

4. Fill up the table by having some possible values of w  and the corresponding areas (A ) .

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Width (w)                                                                                                                         

Area (A)                                                                                                                           

5.  What have you observed about the area (A) in relation to the width (w)?

6.  From the table of values, plot the points and connect them using a smooth curve.

7. What do you observe about the graph?

These are functions that can be described by equations of the form y= ax^2 +bx + c, where a, b, and c are real numbers and a is not equal to 0. The highest power of the variable x is 2. Thus, the equation of a quadratic function is of degree 2.

This lesson introduced quadratic functions. The lesson provides you with opportunities to describe a quadratic function in terms of its equation, graph, and table of values. You were given a chance to compare and see the difference between quadratic functions and linear or other functions.