To find: The rough graph of the parabola of the function , -intercepts of the graph of , -coordinate of the vertex of parabola in terms of and . Confirm the answers by expanding and with the help of formulas.
The graph of the parabola is given in Figure(1) when and . The -intercepts of the graph of are and . The -coordinate of the vertex of parabola in terms of and is equal to .
The function is .
Take a particular case when and . Sketch the graph of the function .
By investigation of the function with the help of graphing calculator, following observations are noted:
|Function||-intercepts of the graph||-intercept of graph||Axis of symmetry|
So, from the observations it can be concluded that the -intercepts of the graph of are and .
From the table, it is visible that the coordinate of the vertex of parabola is .
Now check the results by expanding.
Factorize the function.
So, the -coordinate of vertex of the parabola is .
Now substitute for the -intercepts of parabola.
So, the -intercepts of parabola are and .
Therefore, the -intercepts of the graph of are and . The -coordinate of the vertex of parabola in terms of and is equal to .
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