Friday, November 2, 2012

Graphing Parabola Inequalities

Introduction for graphing parabola inequalities:
Parabola is a conic sections, the intersection of a right circular conical surface and a plane to a generating straight line of that surface.

It is a polynomial function of degree two. A function f : R ? R defined by  the f(x) = ax2 + bx + c, where a, b, c ? R, a ? 0 is called a quadratic function. The graph of a quadratic function is always a parabola inequalities  f(x) > ax2 +  2 , f(x) < ax2 + 2

The graphing for parabola inequalities is shown below.

Example Problem for Graphing Parabola Inequalities:

Ex 1:  Draw the graph of inequalities y > x2

Sol :  Draw x-axis and y-axis on the graph sheet. Mark the scale on x-axis 1 cm = 1 unit and  y-axis 1 cm = 2 units. Assigning value for x = –4 to 4 and we get the corresponding y values:

Plot the points (–4,16), (–3,9), (–2,4),(–1, 1), (0,0), (1,1), (2,4), (3,9), (4,16) on the graph sheet and join the points by smooth curve. This curve is called the parabola y >x2

x  -4  -3  -2 -1  0  1  2  3  4

y  16  9   4    1   0  1  4  9  16


graph of inequalities y > x2

Ex 2:    Draw the graph of  inequalities   y < x2 – 2x – 3.

Sol :    Draw x-axis and y-axis on the graph sheet and mark the scales on x-axis

1 cm = 1 unit and on y-axis 1 cm = 2 units. Assign values x = –4 to 5 and calculate the

Corresponding y values

We plot the points (–4,21), (–3,12), (–2,5), (–1,0), (0, –3), (1, –4), (2, –3), (3,0), (4,5) and

(5,12) on the graph sheet and join these points by a smooth curve. We get a required graph of the parabola y < x2 – 2x – 3

X   -4   -3   -2   -1   0    1   2   3   4  5

Y   21  12   5    0   -3   -4  -3  0   5  12


inequalities   y < x2 – 2x – 3

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Practice Problem for Graphing Parabola Inequalities:

Draw the graph of inequalities   y > x2-1
Draw the graph of  inequalities   y  <  3x2- 4x + 5
3.  Draw the graph of  inequalities   y  <  5x2- 4x + 9
4.  Draw the graph of  inequalities   y > x2+4

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