



 
To find the xintercept, also known as the "zero", or "root" of the equation, set the value of y to 0, and solve the resulting quadratic equation using the quadratic formula. For an equation of the form y = a(x^{2}) + bx + c Where a, b and c are constant numbers (as opposed to variables), the quadratic equation is where ± means (+) OR (). Therefore there are two roots to a quadratic equation, one given by using the (+) and one given by using the (). Therefore there "usually" are 2 yintercept values of a graph involving x^{2}. I say "usually", because you will notice that in the quadratic formula, there is a square root. In general, nothing prevents the value of 4ac from being greater than b^{2}, in which case you would be taking the square root of a negative number, which is not a real number. If this is the case, there are NO yintercepts. Also, you could have the situation where b^{2} = 4ac, in which case you would be adding or subtracting 0 in the quadratic equation. This would mean that there is only one yintercept. Hope this is helpful! Gabe  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 