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
Considering the quadratic function,
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.
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.