Quadratic equations, Quadratic Functions
Many IB Maths Tutors consider quadratic equations as a very important topic of maths. There are the following ways to solve a quadratic equation
► Factorization method
►complete square method
► graphical method
► Quadratic formula method
Quadratic equations, Quadratic Functions, and Quadratic Formula
The quadratic formula is the strongest method to solve a quadratic equation. In this article, I will use a few steps to prove the quadratic formula.
Given equation: ax²+bx+c=0
Step-1: transfer constant term to the right side
Step-2: divide both sides by coefficient of x²
This formula is known as the quadratic formula. We have used a simple way to prove quadratic formula we can put values of a, b and c from any equation and find the value of x (the variable) by directly using this formula.
These types of roots are called Conjugate Roots.
be the common root of ax² + bx + c = 0 & a’x2 + b’x + c’ = 0
Every pair of the quadratic equation whose coefficients fulfills the above condition will have one root in common.
i.e., , , , all these equations can easily be reduced into quadratic equations by applying the method of substitution.
let y= then given equation will become
it’s a simple quadratic equation we can be easily factorized it and solve so y=–3,2
the final equation can be solved using Quadratic formula and the same process can be repeated for y=2
(ii) If a variable is added with it is own reciprocal, then we get a quadratic equation i.e, all these equations can be reduced into quadratic by replacing one term by any other variable.
Standard Form of a Quadratic Function-A quadratic function y=ax2+ bx + c can be
reduced into standard form by the method of completing the square. If we
draw the graph of this function we shall get a parabola with vertex (h,k). The parabola will be upward for a>0 and downward for a<0
Maximum and Minimum value of a quadratic function- If the function is in the form
Then ‘h’ is the input value of the function while ‘k’ is its output.
(i) If a>0 (in case of the upward parabola) the minimum value of f is f(h)=k
f(x) has a minimum value at vertex if a>0 and at
f(x) has a maximum value at vertex if a<0 and at
In the next post about quadratics, I shall discuss discriminant, nature of roots, relationships between the roots. In the meantime, you can download the pdf and solve practice questions