Tag Archives: Quadratic

Axis of Symmetry of Quadratic Graphs

Axis of Symmetry of Quadratic Graphs

The equation of the axis of symmetry of $y=ax^2+bx+c$ is $x=-\dfrac{b}{2a}$. Example 1 Find the equation of the axis of symmetry of $y=x^2+4x-2$. \( \begin{align} \displaystylex &= -\dfrac{b}{2a} \\&= -\dfrac{4}{2 \times 1} \\\therefore x &= -2\end{align} \) Example 2 Find the equation of the axis of symmetry of $y=-2x^2-12x+3$. \( \begin{align} \displaystylex &= -\dfrac{b}{2a} \\&= […]

Quadratic Optimisation

Quadratic Optimisation

The process of finding the maximum or minimum value of 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 $x=-\dfrac{b}{2a}$ $a<0$: the maximum value of $y$ occurs at $x=-\dfrac{b}{2a}$ We need to identify a situation’s maximum or minimum […]

Solving Quadratic Equations by Quadratic Formula

Solving Quadratic Equations by Quadratic Formula

In many cases, factorising a quadratic equation or completing the square can be long or difficult. We can instead use the quadratic formula. \( \begin{align} \displaystyle \require{AMSsymbols} \require{color}ax^2 + bx + c &= 0 \\ax^2 + bx &= -c \\x^2 + \dfrac{b}{a}x &= -\dfrac{c}{a} \\x^2 + \dfrac{b}{a}x \color{red} + \Big(\dfrac{b}{2a}\Big)^2 &= -\dfrac{c}{a} \color{red} + \Big(\dfrac{b}{2a}\Big)^2\\\Big(x+\dfrac{b}{2a}\Big)^2 […]