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
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
Having problem with math solver for free keep reading my upcoming posts, i will try to help you.
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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