## Quadratic Equations Study Guide: Homework Help

How do I determine if a funtion is quadratic?

A quadratic function, is a polynomial function of the form `f(x) = ax^2 + bx + c, x!= 0.` Therefore, if your function has an `"x^2"`  term, then it is a quadratic function.

Consider a polynomial function `P(x)=ax^2+bx+c,a!=0` The degree of P(x) is 2. Thus P(x) is quadratic polynomial. Also it can be said that P(x) is quadratic function. To determine if function is quadratic, first check if function is polynomial, second ceheck its degree if degree is 2 then...

Factorise the expression  `x-1 - (x-1)^2`

Follow the steps 1)-4) 1) First expand out the bracketed term: `x-1 -(x-1)^2 = x- 1 - (x-1)(x-1) ` `= x - 1 - (x^2 - x - x + 1)` `= x - 1 - (x^2 - 2x + 1)` 2) Now gather terms: `x - 1 - (x-1)^2 = x - 1 - x^2 + 2x - 1 = -x^2 + 3x - 2` 3) Now, to factorise the original expression, we are looking...

Alternatively, factor out an `x-1` right away. `x-1-(x-1)^2=(x-1)(1-(x-1))` `=(x-1)(1-x+1)=(x-1)(2-x).`