Graphing Quadratic Function

Mehthod to graph the quadratic equations and functions $ax^2+bx+c$

To draw the graph of any quadratic function , find out the pair of values of points (x,y) which satisfy the given equation

Then plot those points onto the graph , the graph of quadratic function $ax^2+bx+c$ is parabolic

The point is called the vertex of the parabola

$\left( {\frac{{- b}}{{2a}},\frac{{4ac-b^2}}{{4a}}}\right)$

The abscissas of the points of intersection of parabola y= $ax^2+bx+c$ gives the roots of the quadratic equation $ax^2+bx+c$

Example , Draw the graph of quadratic polynomial $x^2+5x+6$

We have to find various points for (x,y) which satisfy the function

The graph of equation has been drawn below

The points at which the graph cross x axis are the roots of the quadratic equation , those are points x = -2 , -3 as we can see those in graph

The value of a = 1 which is greater then 0 , a>o so the graph is parabolic of upward shape

The point is called the vertex of the parabola

$\left( {\frac{{- b}}{{2a}},\frac{{4ac-b^2}}{{4a}}}\right)$

These are X = -2.5 and Y = -0.25

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