Previously we have discussed about antiderivative of sinx and In todays lesson we are going to study about Parabolic functions, vertex, axis of symmetry, which comes under Grade XI of maharashtra secondary board.
First we are going to learn about parabolic functions and also learn to solve math problems related to it.
What are parabolic functions?
Parabolic functions is the path traced by a point which moves in a plane I such a way that its distance from a fixed point is always equal to its distance from a fixed line,both lying in the n fixed point does not lie on the given line.
The fixed point is called as the focus of the parabola and the fixed line is called its directrix.
Aline through the focus and perpendicular to the directrix is called the axis of parabola.the poit of intersection of the parabola with its axis is called the vertex of parabola.
There are four forms of parabola
The first standard form or the rigt handed parabola is given by the formula
Y2=4ax, where a>0
The second form of standard parabola or left handed parabola I sgiven by the formula
Y2=-4ax, where a>0
The third ofrm of parabola is also known as upward parabola an dis given by the equation
X2=4ay where a>0
The last form of parabola is called as the downward parabola
It is given by the formula
X2=-4ay where a>0
Now we move to the second topic of grade XI called as the vertex
What is vertex?
In mathematics ,a vertex most commonly refers to a corner or endpoint where lines meet.it can also refer to the maximum or minimum point on a parabola along its line of symmetry.
Like we can take an example of a triangle which has three vertices.
A parabola's equation can take two different forms. The first, vertex form, is represented as y= a(x-h)²+k, where x and y are the coordinates for individual points on the parabola, a is the scalar that can change the shape and direction of of the parabola, and h and k are the vertex points. The parabola's standard form equation, represented as y = ax² + bx + c, focuses on the parabola's direction and its axis of symmetry, which is the line that bisects the parabola. Converting from the vertex to the standard form can make the equation more easy for other calculations.
Now we come to other topic for the Grade XI which is called as the axis of symmetry
Every parabola has an axis of symmetry which is the line that runs down its “centre”.this line divided the graph into two perfect halves.
To find the axis of symmetry we can use two different formulas.one fomula works when the parabola’s equation is in vertex form and the other works on the parabola’s equation is in the standard form.(want to Learn more about Axis of Symmetry,click here),
If the equation is in the vertex form then the axis of it is x=h in general vertex form equation y=(x-h)2 +k
If the equation is in standard form,then the formula is x=-b/2a from the general standard form equation y=ax2 + bx +c
We have now deep knowledge about the parabolic functions, vertex and axis of symmetry and if anyone want to know about Measures of central tendency
then they can refer to internet and text books for understanding it more precisely. You can also refer Grade XII blog for further reading on Conditional statements.
First we are going to learn about parabolic functions and also learn to solve math problems related to it.
What are parabolic functions?
Parabolic functions is the path traced by a point which moves in a plane I such a way that its distance from a fixed point is always equal to its distance from a fixed line,both lying in the n fixed point does not lie on the given line.
The fixed point is called as the focus of the parabola and the fixed line is called its directrix.
Aline through the focus and perpendicular to the directrix is called the axis of parabola.the poit of intersection of the parabola with its axis is called the vertex of parabola.
There are four forms of parabola
The first standard form or the rigt handed parabola is given by the formula
Y2=4ax, where a>0
The second form of standard parabola or left handed parabola I sgiven by the formula
Y2=-4ax, where a>0
The third ofrm of parabola is also known as upward parabola an dis given by the equation
X2=4ay where a>0
The last form of parabola is called as the downward parabola
It is given by the formula
X2=-4ay where a>0
Now we move to the second topic of grade XI called as the vertex
What is vertex?
In mathematics ,a vertex most commonly refers to a corner or endpoint where lines meet.it can also refer to the maximum or minimum point on a parabola along its line of symmetry.
Like we can take an example of a triangle which has three vertices.
A parabola's equation can take two different forms. The first, vertex form, is represented as y= a(x-h)²+k, where x and y are the coordinates for individual points on the parabola, a is the scalar that can change the shape and direction of of the parabola, and h and k are the vertex points. The parabola's standard form equation, represented as y = ax² + bx + c, focuses on the parabola's direction and its axis of symmetry, which is the line that bisects the parabola. Converting from the vertex to the standard form can make the equation more easy for other calculations.
Now we come to other topic for the Grade XI which is called as the axis of symmetry
Every parabola has an axis of symmetry which is the line that runs down its “centre”.this line divided the graph into two perfect halves.
To find the axis of symmetry we can use two different formulas.one fomula works when the parabola’s equation is in vertex form and the other works on the parabola’s equation is in the standard form.(want to Learn more about Axis of Symmetry,click here),
If the equation is in the vertex form then the axis of it is x=h in general vertex form equation y=(x-h)2 +k
If the equation is in standard form,then the formula is x=-b/2a from the general standard form equation y=ax2 + bx +c
We have now deep knowledge about the parabolic functions, vertex and axis of symmetry and if anyone want to know about Measures of central tendency
then they can refer to internet and text books for understanding it more precisely. You can also refer Grade XII blog for further reading on Conditional statements.
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