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# Quadratic in the polynomial form

## on Jul 02, 2010

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## Quadratic in the polynomial formPresentation Transcript

• School level : SHS 2 Curriculum area: Elective Maths Class time : 80min (two periods)
• Determine how changes in the parameters of a quadratic equation in the polynomial form affect the graph
• Determine how to use the polynomial form of a polynomial quadratic equation to find the location of the vertex on a graph.
• Apply the vertex of a quadratic function in a realistic setting.
• Think of the following scenarios and describe the path when:
• a golf ball is played at one end of a park to another
• A basketball is thrown with the aim of scoring
• (You can sketch the path on a sheet of paper)
• In both scenarios, the path described by the ball will follow a graph such as
EXPECTED RESPONSE 30 0 40m/s
• y=ax 2 +bx +k.
• What are the parameters of the quadratic function?
• The nature of the graph
• The nature of the quadratic curve when a is either positive or negative or zero. Graph 1
• The nature of the graph when the absolute value of a is either increasing or decreasing. [ [click here ), check here too
• ]]]]
• The effects of the value of k on the quadratic curve. That is increasing and decreasing the value of k . click here
• The effects of the value of b on the quadratic curve. Click
• Determination of the axis of symmetry and its corresponding y value.
• CONCLUSION
• Quadratic function in the form y = ax 2 + bx + k becomes wider as | a | decreases and narrower as | a | increases.
• The parabola opens up when a > 0 and opens down when a < 0.
• The leading coefficient a is the only coefficient that changes the shape of the graph.
• The position of the vertex is determined by varying the value of b . If b>0, the vertex is located on the left of the y -axis. If b<0, the vertex is located on the right of the y -axis.
• If b=0, the vertex is located on the y -axis. The x coordinate of the vertex is given by and the y coordinate can be found by substituting the value x in the quadratic equation. The axis of symmetry is .
• Increasing or decreasing the value of k moves the graph up or down vertically without altering the shape.