 The process of finding the maximum or minimum value of a functions is called optimisation. For the quadratic function $y=ax^2+bx+c$, we have already seen that the vertex has $x$-coordinate $-\dfrac{b}{2a}$. $a>0$: the minimum value of $y$ occurs at $x=-\dfrac{b}{2a}$ $a # Positive Definite Negative Definite The Discriminant and the Quadratic Graph The discriminant of the quadratic equation$ax^2+bx+c=0$is$\Delta = b^2-4ac$. We used the discriminant to determine the number of real roots of the quadratic equation. If they exist, these roots correspond to$x$-intercepts of the quadratic$y = ax^2+bx+c$. The discriminant tells us about the relationship between a [...] # Discriminant The formula$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$gives the solutions to the general quadratic equation$ax^2+bx+c=0$. By examining the expression under the square root sign,$b^2-4ac$, we known as the discriminant, symbol used is$\Delta$. The quadratic formula becomes$x=\dfrac{-b + \sqrt{\Delta}}{2a}$and$x=\dfrac{-b - \sqrt{\Delta}}{2a}$.$\Delta 0\$ If the discriminant is positive there are [...]  