Quadratic function can be present in the standard form which is
or it can be present in the vertex form which is
. Remember that
and
here are real numbers and
.
Direction of opening of graph is dependent on the value of
. If a>0 then graph opens upwards and if a<0 then graph opens downwards.
We will try sketching basic graph
where
.
Note that we can write
in vertex form as
and we can also write it in standard form as
To plot graph of
. We will take some random values of
and will find corresponding values of y.
Now we can try sketching the graph
where a=-1. We will be taking some random values of
and finding corresponding values of
. You will have these table of values. By using these table of values, we can have graph shown right below the table. Clearly, this graph is opening downwards. This is because a<0.
Now we will try plotting
. Table of values would be
Now we can plot these points and can get the shape of the graph. You see that it is going to be opening upwards because a>0.
Now at least, you can know the direction of opening of graph of a given quadratic function without actually plotting the graph.
Upwards
Upwards
Downwards
Upwards
Downwards
Downwards
Upwards
Downwards
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