Quadratic Equations and Graph
Short Questions
Define quadratic and cubic function with example.
Quadratic function - A function of the form f(x) = ax2 + bx + c; a ≠ 0 is called quadratic function. For example: f(x) = 2x2 + 3, f(x) = 5x2 - 7x + 9.
Cubic function - A function of the form f(x) = ax3 + bx2 + cx + d; a ≠ 0 is called cubic function. For example: f(x) = 5x3 + 3x2, f(x) = 8x3.What is parabola?
The graph of quadratic equation y = ax2 + bx + c is called parabola.
Define vertex of parabola.
The turning point of the parabola is called the vertex of parabola.
The vertex of parabola y = ax2 + bx + c is
The vertex of parabola y = ax2 + bx + c is
In a quadratic equation ax2 + bx + c = 0, what a, b and c are called?
In a quadratic equation ax2 + bx + c = 0, a is the coefficient of x2, b is the coefficient of x and c is the constant term.
Define line of symmetry in parabolic curve.
A vertical line that divides the parabola into two congruent halves is called line of symmetry.
Write the equation of line of symmetry in the equation y = x2.
The vertex of y = x2, (h, k) is (0, 0) so the line of symmetry is x = 0.
Write the equation of line of symmetry in the equation y = ax2 + bx + c.
The equation of line of symmetry in the equation y = ax2 + bx + c is x = -
Write the vertex of the equation y = a(x - h)2 + k.
The vertex of the equation y = a(x - h)2 + k. is (h, k).
Some notes on parabola, y = ax2 + bx + c:
- The parabola turns upward for a > 0 and turns downward for a < 0.
- Greater value of a numerically narrower will be the faces of parabola and lesser the value of a numerically wider will be the faces of parabola.
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If c > 0 then the vertex is c units above the origin.
If c < 0 then the vertex is c units below the origin.