To find the coefficients in quadratic equations written in factored form, let's break it down step by step.

We start with this general equation:

$y = a(x - p)(x - q)$

In this equation:

• $p$ and $q$ are the roots (the points where the graph touches the x-axis).
• $a$ is the number in front of $x^2$, also known as the coefficient.

Step 1: Expand the expression

To find the coefficients $a$, $b$, and $c$, we need to expand the factored form.

For example, let’s look at:

$y = 2(x - 3)(x - 1)$

Step 2: Multiply it out

First, we need to multiply the two parts in parentheses:

$(x - 3)(x - 1) = x^2 - 4x + 3$

Next, we’ll multiply the result by $2$:

$y = 2(x^2 - 4x + 3) = 2x^2 - 8x + 6$

Step 3: Identify coefficients

Now, we can easily find the coefficients:

• $a = 2$
• $b = -8$
• $c = 6$

So, always remember to expand the equation before you look for the coefficients!