Solving Quadratic Equations Flashcards
What is a quadratic equation in standard form?
a(x^2) + bx + c = 0
How can you solve quadratic equations using factorising?
If you get the equation into the form (ax - b)(cx - d) = 0 then the two solutions are b/a and d/c as one of the two brackets must be equal to zero.
What is the quadratic formula?
x = {-b (+/-) rt2[(b^2) - 4ac]}/2a
How can you solve quadratic equations using the quadratic formula?
You simply put the equation into standard form and follow the equation through. You get the two solutions.
How can you solve a quadratic equation by completing the square?
(x + b/2)^2 expands to x^2 + bx + (b/2)^2. This allows us to rearrange x^2 + bx + c = 0 into (x + b/2)^2 - (b/2)^2 + c = 0 and then to (x + b/2)^2 = (b/2)^2 + c. You can then square root both sides.
What can be said about graphs of quadratic functions?
All quadratic functions have a line of symmetry on their graph. In a function y = a(x^2) + bx + c then if a > 0 then it has a minimum turning point and if a < 0 then it has a maximum turning point.
The points where the graph crosses the x axis are the solutions.
How can you find the turning point and line of symmetry for a quadratic function?
You firstly complete the square in the quadratic function so you end up with (x + a)^2 + b. The smallest possible value for (x + a)^2 is 0 when x = -a. That will therefore be the equation for the line of symmetry. If the term is 0, the whole expression will have a value of b giving the coordinates (-a, b).
How do you solve formulae using iteration?
Firstly, you rearrange the equation to leave x on its own on one side of the equation. You then use an iterative formula where [x(n+1)] = (rt2{-c - b[x(n)]})/a in the case of a quadratic equation.
