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.
Stuck on any of these topics How to Find Asymptotes, Dot Product Calculator try out some best online tutoring math website.
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.
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.
Stuck on any of these topics How to Find Asymptotes, Dot Product Calculator try out some best online tutoring math website.
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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