Graph Parabola Equation

Introduction to graph parabola equation:

The parabola is a member of conic section which means the intersection of a cone with a plane.
The general equation of a parabola is given as  (Ax + By)2 + Cx + Dy + E = 0.
It is very simple to graph parabola equation. To graph parabola equation, we have to find vertex, x  and y intercepts. The steps for graphing parabola equations are given below with an example problem.

Steps to Graph Parabola Equation:

Step 1: Allocate the variables a, b and c from the given equation

Step 2: Check and determine whether the parabola opens upwards or downwards.

If a > 0, then the parabola opens upwards (U-shaped).

If a < 0, then the parabola opens downwards (n-shaped)

Step 3: To find vertex:

The next step is to find vertex. To find vertex, we have to find the x-coordinate of the maximum point (or minimum point) by

X = - `b/(2a)`

By substituting this x-value into the given quadratic function i.e., the y expression, we obtain y-coordinate.

The obtained coordinate (X, Y) is the vertex of the parabola.

Step 4: To find the coordinates of the y-intercept.

By substituting x = 0 in the expression, we can find the y-intercept coordinate.

Step 5: To find the coordinates of the x-intercept.

By substituting y = 0 in the expression and solving the quadratic equation, we can find x-intercept coordinate.

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Example Problem to Graph Parabola Equation:

Graph the equation y = x2 - 7x +12.

Step 1:  Allocate the variables a, b and c from the given equation

a = 1

b = - 7

c = 12

Step 2: In the given equation, a is greater than 0 ( a = 1), therefore the graph of given equation is a parabola opens upwards (U-shaped) i.e., it has minimum point.

Step 3:  To find the vertex

x = - `b/(2a)` .

=  -`(-7)/(2(1))` .

= `7/2` .

= 3.5 

Y has the minimum point. So,

y = (3.5)2 - 7(3.5) + 12

= 12.25 - 24.5 + 12

= -0.25

Therefore, the minimum point obtained is (3.5, - 0.25)

Step 4: To find y-intercept.

By substituting x = 0 in the given equation y = x2 - 7x + 12, we get

y = (0)2 - 7(0) + 12 = 12

So, y intercept = (0, 12)

Step 5: To find x-intercept.

By substituting y = 0 in the given equation y = x2 - 7x + 12, we get

0 = x2 - 7x + 12

By factoring the above equation, we get

x = 3,  x = 4

The graph is drawn below with the help of the above information.  

   

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