The Quadratic Formula, which is written as

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

is really important in Year 10 Math. It especially helps when drawing parabolas. Once you understand how this formula works, graphing quadratic equations becomes much easier!

What is a Quadratic Equation?

A quadratic equation usually looks like this:

$ax^2 + bx + c = 0$

In this equation, $a$, $b$, and $c$ are numbers, and $a$ cannot be zero. When you graph this equation, it makes a shape called a parabola. This shape can either open up or down, depending on whether $a$ is positive or negative.

How Does the Formula Help?

1. Finding Roots: The Quadratic Formula helps us find the x-values (also known as roots) where the parabola touches the x-axis. Finding these roots is important for drawing the graph correctly.

2. Vertex Calculation: We can also find the x-coordinate of the highest or lowest point of the parabola (called the vertex) with the formula $-b/(2a)$. This point is key to understanding how the parabola looks.

Example:

Let's look at the quadratic equation:

$2x^2 + 4x - 6 = 0$

Here, we can see that $a = 2$, $b = 4$, and $c = -6$. We can use the Quadratic Formula with these values to find the roots:

$$x = \frac{-4 \pm \sqrt{4^2 - 4 \cdot 2 \cdot (-6)}}{2 \cdot 2}$$

When we solve this, we will get two x-values. These values will help us draw the parabola accurately!

Using the Quadratic Formula is like a tool that helps you connect algebra with drawing graphs. It's a powerful addition to your Year 10 math skills!