When you’re in Year 12 and need to solve quadratic equations, there are a few methods you should know. Each method has its own way of helping, so you can choose what works best for you. Here’s a quick overview:
Factoring: This method lets you break down the quadratic into simpler parts. You can often rewrite it like this: (ax^2 + bx + c = (px + q)(rx + s)). If you can factor it nicely, it makes solving the equation much easier!
Completing the Square: This technique changes a quadratic into a perfect square trinomial. It’s really useful if you want to find the peak point of the graph (called the vertex) or if you need to solve the equation (ax^2 + bx + c = 0) by rewriting it as ((x - p)^2 = q) and then finding (x).
Quadratic Formula: This is probably the most well-known method. The formula is (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}). You can use this for any quadratic equation, and it really helps when factoring gets tough.
Graphing: While this method might not always give you the exact answers, drawing the graph of the quadratic can help you see where it crosses the x-axis. This can give you a good idea of the possible answers.
Try out these methods, and see which ones you like best!
When you’re in Year 12 and need to solve quadratic equations, there are a few methods you should know. Each method has its own way of helping, so you can choose what works best for you. Here’s a quick overview:
Factoring: This method lets you break down the quadratic into simpler parts. You can often rewrite it like this: (ax^2 + bx + c = (px + q)(rx + s)). If you can factor it nicely, it makes solving the equation much easier!
Completing the Square: This technique changes a quadratic into a perfect square trinomial. It’s really useful if you want to find the peak point of the graph (called the vertex) or if you need to solve the equation (ax^2 + bx + c = 0) by rewriting it as ((x - p)^2 = q) and then finding (x).
Quadratic Formula: This is probably the most well-known method. The formula is (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}). You can use this for any quadratic equation, and it really helps when factoring gets tough.
Graphing: While this method might not always give you the exact answers, drawing the graph of the quadratic can help you see where it crosses the x-axis. This can give you a good idea of the possible answers.
Try out these methods, and see which ones you like best!