Quadratic Function Presentation Essay Example

• A quadratic function (f) is a function that has the form as f(x) = ax2 + bx + c where a, b and c are real numbers and a not equal to zero (or a ≠ 0). • The graph of the quadratic function is called a parabola. It is a "U" or “n” shaped curve that may open up or down depending on the sign of coefficient a. Any equation that has 2 as the largest exponent of x is a quadratic function.

☺Forms of Quadratic functions:
* Quadratic functions can be expressed in 3 forms: 1. General form: f (x) = ax2 + bx + c 2. Vertex form: f (x)= a(x - h)2 + k (where h and k are the x and y coordinates of the vertex) 3. Factored form: f(x)= a(x - r1) (x - r2)

1. General form
• Form : f(x) = ax2+ bx+ c • General form is always written with the x2 term first, followed by the x term, and the constant term last. a, b, and c are called the coefficients of the equation. It is possible for the b and/or c coefficient to equal zero. Examples of some quadratic functions in standard form are: a. f(x) = 2x2 + 3x – 4 (where a = 2, b = 3, c = -4) b. f(x) =x2 – 4 (where a = 1, b = 0, c = -4) c. f(x)= x2 ( where a = 1, b and c = 0) d. f(x)= x2 – 8x (where a = ½, b = -8, c = 0).

2. Vertex Form
• Form: f(x) = a(x - h)2 + k where the point (h, k) is the vertex of the parabola. • Vertex form or graphing form of a parabola. • Examples: a. 2(x - 2)2 + 5 (where a = 2, h = 2, and k = 5) b. (x + 5)2 (where a = 1, h = -5, k = 0)

3.Factored Form
• Form: a(x - r1) (x - r2) where r1 and r2 are the roots of the equation. • Examples: a. (x - 1)(x - 2) b. 2(x - 3)(x - 4) or (2x - 3)(x - 4)

Discriminant
• Quadratic formula: If ax2 + bx + c, a ≠ 0, x = • The value contained in the square root of the quadratic formula is called the discriminant, and is often represented by ∆ = b2 – 4ac. * b2 – 4ac > 0 → There are 2 roots x1,2= * b2 – 4ac = 0 * b2 – 4ac < 0 → → There is 1 real root, x = -b/2a. There are no real roots. .

Using Quadratic Formula
• A general formula for solving