Quadratic Equations and Graph
Short Questions
Define quadratic and cubic function with example.
Quadratic function  A function of the form f(x) = ax^{2} + bx + c; a ≠ 0 is called quadratic function. For example: f(x) = 2x^{2} + 3, f(x) = 5x^{2}  7x + 9.
Cubic function  A function of the form f(x) = ax^{3} + bx^{2} + cx + d; a ≠ 0 is called cubic function. For example: f(x) = 5x^{3} + 3x^{2}, f(x) = 8x^{3}.What is parabola?
The graph of quadratic equation y = ax^{2} + 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 = ax^{2} + bx + c is $(\frac{b}{2a}, \frac{4ac \,  \, b^2}{4a})$
The vertex of parabola y = ax^{2} + bx + c is $(\frac{b}{2a}, \frac{4ac \,  \, b^2}{4a})$
In a quadratic equation ax^{2} + bx + c = 0, what a, b and c are called?
In a quadratic equation ax^{2} + bx + c = 0, a is the coefficient of x^{2}, 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 = x^{2}.
The vertex of y = x^{2}, (h, k) is (0, 0) so the line of symmetry is x = 0.
Write the equation of line of symmetry in the equation y = ax^{2} + bx + c.
The equation of line of symmetry in the equation y = ax^{2} + bx + c is x = $\frac{b}{2a}$
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 = ax^{2} + 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.

If c > 0 then the vertex is c units above the origin.
If c < 0 then the vertex is c units below the origin.