Parabola Graph

Parabola is a curve and whose equation is in the form of f(x) = ax2+bx+c, which is the standard form of a parabola. To draw a parabola graph, we have to first find the vertex for the given equation. This can be done by using x=-b/2a and y = f(-b/2a). Plotting the graph, when the quadratic equation is given in the form of f(x) = a(x-h)2 + k, where (h,k) is the vertex of the parabola, is its vertex form. Find all the parabola formulas for vertex, focus and directrix here.

We know, in quadratic equation f(x) = ax2 + bx + c, a b and c are the constants and x is the variable. So, by finding the different values of x and corresponding values of y or f(x), we can plot all the points in the graph and by joining all of them we can get the required shape. Now let us learn how to graph a parabola.

Also, read:

How to Graph Parabola

Two points define any line. Since parabola is a curve-shaped structure, we have to find more than two points here, to plot it. We need to determine at least five points as a medium to design a pleasing shape. In the beginning, we draw a parabola by plotting the points.

Suppose we have a quadratic equation of the form y=ax2+ bx+c, where x is the independent variable and y is the dependent variable. We have to choose some values for x and then find the corresponding y-values. Now, these values of x and y values will provide us with the points in the x-y plane to plot the required parabola. With the help of these points, we can sketch the graph.

Let us understand with the help of examples.

Graphing Parabola Examples

Example 1: Draw a graph for the equation y = 2x2 + x+ 1.

Solution: The given equation is y = 2x2 + x+ 1.

Here, a = 2, b = 1 and c = 1.

It needs to find the vertex now

x = -b/(2a)

x = -1/(2(2))

x = -1/ 4

x = -0.25

Now putting x = -0.25 in the equation y= 2x2 + x+ 1

y= 2(-0.25)2 + (-0.25)+ 1.

y = 2(0.0625) – 0.25+1

y = 0.125 – 0.25 +1

y = 0.875

Now putting the different values for x and calculate the corresponding values for y.

When x = 1 ⇒ y= 2x2 + x+ 1 ⇒ y = 2(1)2+ 1 + 1 ⇒ y = 2+ 1 + 1 ⇒ y = 4

When x = 2 ⇒ y= 2x2 + x+ 1 ⇒ y = 2(2)2+ 2 + 1 ⇒ y = 8+ 2 + 1 ⇒ y = 11

When x = 3 ⇒ y= 2x2 + x+ 1 ⇒ y = 2(3)2+ 3 + 1 ⇒ y = 18+ 3 + 1 ⇒ y = 22

When x = -1 ⇒ y= 2x2 + x+ 1 ⇒ y = 2(-1)2– 1 + 1 ⇒ y = 2- 1 + 1 ⇒ y = 2

When x = -2 ⇒ y= 2x2 + x+ 1 ⇒ y = 2(-2)2– 2 + 1 ⇒ y = 8- 2 + 1 ⇒ y = 7

When x = -3 ⇒ y= 2x2 + x+ 1 ⇒ y = 2(-3)2– 3 + 1 ⇒ y = 18 -3 + 1 ⇒ y = 16

Hence,

x

1

2

3

-1

-2

-3

y

4

11

22

2

7

16

Plot all the points and join the plotted points.

Parabola Graph Example

Example 2: Draw a graph for the equation y = 2x2.

Solution:

The given equation is y= 2x2.

Here a = 2, b = 0 and c = 0.

It needs to find the vertex now

x = -b/(2a)

x = 0

Now putting x = 0 in the equation y= 2x2.

y= 2x2

y = 2(0)2

y = 0

Now putting in different values for x and calculate the corresponding values for y.

When x = 1 ⇒ y= 2x2⇒ y = 2(1)2 ⇒ y = 2

When x = 2 ⇒ y= 2x2⇒ y = 2(2)2⇒ y = 8

When x = 3 ⇒ y= 2x2⇒ y = 2(3)2⇒ y = 18

When x = -1 ⇒ y= 2x2⇒ y = 2(-1)2⇒ y = 2

When x = -2 ⇒ y= 2x2⇒ y = 2(-2)2⇒ y = 8

When x = -3 ⇒ y= 2x2⇒ y = 2(-3)2⇒ y = 18

Hence,

x

1

2

3

-1

-2

-3

y

2

8

18

2

8

18

Plot all the points and join the plotted points.

Graphing Parabola Examples

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