The Quad

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A quadratic function is a function of the form

f(x) = ax2 + bx + c

where a, b and c are real numbers and a is not equal to zero(0). The graph of the quadratic function is called a parabola. It is a U shaped curve that may open up or down depending on the sign of coefficient a.

x2+ x+ =0

The area bounded by the curve above the x-axis is: sq. units.
The value of the curve occurs at co-ordinates: .
  

The Quadratic Equation

x =
-b +  sqrt(b2-4ac)
2a
b2-4ac  is called the discriminant (d).
You can use the discriminant (d) to determine what kind of solutions to look for:
  • If d > 0 then there are two distinct solutions: positive and negative.
  • If d > 0 and a perfect square then there are two distinct rational solutions: positive and negative.
  • If d = 0 then there is one rational solution.
  • If d < 0 then there are no rational solutions (because you cannot take the square root of a negative number).In other words, there are no x intercepts.

Tally Sheet

Adventures in
Mathematics

by K R Hubbell

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