Vertex form of Quadratic Functions is
. It tells a lot about quadratic function.
Vertex of this quadratic function is at
.
can tell you about direction of opening of graph of given quadratic function. If
, direction of opening is upwards and if
then direction of opening is downwards.
can also give you idea about width of the graph.
Axis of symmetry of quadratic function is a vertical line which divides graph of quadratic function into two equal parts. Equation of axis of symmetry can be easily obtained from vertex form which is
. We will cover this using examples as well.
Domain of quadratic function which is of the form
is always all real numbers.
Range of quadratic function which is of the form
depends on two situations. If direction of opening of quadratic function is upwards (if a>0) then range is
.
If direction of opening of quadratic function is downwards (if a<0) then range is
. This concept will be more clear when we practice plotting of quadratic functions.
Consider an example, we have quadratic function
, can you find out following things?
vertex?
direction of opening?
axis of symmetry?
domain?
range?
Comparing quadratic function
with vertex form
, we get
and
.
We know that vertex is equal to =
. Therefore, vertex is equal to (3 , 5).
We know that direction of opening depends on value of
. If a>0 then direction of opening is upwards and if a<0 then direction of opening is downwards. In this case, we have
. Therefore, direction of opening is upwards.
Equation of Axis of symmetry is equal to
. In this case, we have equation of axis of symmetry equal to
.
Domain is all real numbers.
Range in this case would be
because direction of opening is upwards. Therefore, we have range equal to
.
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