X-Std. : MATHS
GRAPH: QUADRATIC GRAPHS
Introduction:
The trajectory followed by an object (say, a ball) thrown upward at an angle gives a curve known as a parabola. Trajectory of water jets in a fountain or of a bouncing ball results in a parabolic path.
A parabola represents a Quadratic function.
A quadratic function has the form f(x)= ax2+ bx+c. where a, b,c are constants.
Finding the Nature of Solution of Quadratic Equations Graphically:
To obtain the roots of the quadratic equation ax2+bx+c=0 graphically. we first how the graph of y=ax2+bx+c.
The solutions of the quadratic equation are the coordinates of the points of Intersection of the curve with X axis.
To determine the nature of solution of a quadratic equation, we can use the following procedure.
1) If the graph of the given quadratic equation intersect the axis at two distinct points, then the given equation has two real and unequal roots.
2) If the graph of the given quadratic equation touch the X axis at only one point then the given equation has only one root which is same as saying two real and equal roots.
3) If the graph of the given equation does not intersect the X axis at any point then the given equation has no real root.
Solving quadratic equations through Intersection of lines:
We can determine roots of a quadratic equation graphically by choosing appropriate parabola and intersecting it with a desired straight line.
(i) If the straight line intersects the parabola at two distinct points, then the x coordinates of those points will be the roots of the given quadratic equation.
(ii) If the straight line just touch the parabola at only one point, then the a coordinate of the common point will be the single root of the quadratic equation.
(iii) If the straight line doesn't intersect or touch the parabola then the quadratic equation will have no real roots.
Notes:
1). If all the terms of the quadratic equations are +ve, then it is enough to take x values from -3 to +3. If the equation starts with 2x2, then also the same values.
2). If the coefficient of x is 0 or if the coefficient of x is +ve and the constant term is -ve then it is enough to take x values from -4 to +4 and omit those values not necessary to plot.
3). If the coefficient of x is -ve, then it is enough to take x values from -4 to +4 and omit those values not necessary to plot.
GRAPH:
QUADRATIC GRAPHS
English Medium
KALVIASIRIYARKAL
kalviasiriyarkal.blogspot.com
Prepared by : """"""""""""""""""""
Mr. L.Sankara Narayanan.,
M.A.,B.SC.,B.Ed.,M.Phil.,
AHM.,
G.S.HINDU HR.SEC.SCHOOL.,
Srivilliputhur.
KALVIASIRIYARKAL
kalviasiriyarkal.blogspot.com
: QUADRATIC GRAPHS. Finding the Nature of Solution of Quadratic Equations Graphically: (EM)){kind=link}
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