2 or 2 , are called quadratic functions. 6 y e y x How can - PowerPoint PPT Presentation

D AY 121 – U NDERSTANDING THE PARTS OF A Q UADRATIC WITH R EAL W ORLD D ATA AND WRITE THE E QUATION

The relationship involves the square of the length of an edge. Functions that involve squaring, such as 2 or   2 , are called quadratic functions. 6 y e y x How can you use this pattern to find how much paint you need to paint cubes of different sizes?

Find out how much paint is needed to cover 1 sq unit, and multiply that amount of paint by the surface area, which is 6e 2

The following spreadsheet shows the data for the flight of a small rocket. The graph of this data, which has a quadratic relationship, is called parabola. Use the data from the spreadsheet to draw a graph. The curve is a parabola that opens downward. You can see that the rocket reaches its maximum height of 784 feet, after 7 seconds. A parabola may open either downward or upward. The point where the curve changes direction is the vertex.

Edges and Surface Area Suppose you are going to paint all six faces of a cube. Guess how much paint will be needed if you decide to double the length of each edge. You might be surprised to find that it will take more than twice the amount to paint the faces of the larger cube. Suppose the edge of a cube is 1 meter. Since the area of each face is 1 square meter (1m 2 ), the surface area of the six faces is 6 m 2 . Examine how the surface area of the six faces grows as the length of each edge is increased.

1.Compare the surface of a 1-meter cube with the surface area of a 2-meter cube. What happens to the surface area of the 6 faces when the length of the edge doubles? 2.Examine a cube whose edge is triple the length of the first cube’s edge. What happens to the surface area of the 6 faces when the length of the edge triples?

1.Compare the surface of a 1-meter cube with the surface area of a 2-meter cube. What happens to the surface area of the 6 faces when the length of the edge doubles? Answers may vary 2.Examine a cube whose edge is triple the length of the first cube’s edge. What happens to the surface area of the 6 faces when the length of the edge triples? the surface area is 9 times larger.

3. Examine the surface-area patterns for the 6 faces of the 1-,2-, and 3-meter cubes. What is the ratio of the surface area of a 2-meter cube to the surface area of a 3-meter cube? How does this ratio relate to the ratio of the edge lengths of the two cubes? 4. Extend the following table to include an edge length of 5 meters. Notice the pattern.

3. Examine the surface-area patterns for the 6 faces of the 1-,2-, and 3-meter cubes. What is the ratio of the surface area of a 2-meter cube to the surface area of a 3-meter cube? How does this ratio relate to the ratio of the edge lengths of the two cubes? 24:54 , 6(2) 2 : 6(3) 2 4. Extend the following table to include an edge length of 5 meters. Notice the pattern.

5. Write the formula for the total surface area of the 6 faces of a cube based on the pattern that you see in the table.

5. Write the formula for the total surface area of the 6 faces of a cube based on the pattern that you see in the table. S = 6e 2