When you're working with quadratic equations, there are some great ways to find the coefficients fast.

A quadratic equation usually looks like this:

$$y = ax^2 + bx + c$$

In this equation, $a$, $b$, and $c$ are the coefficients you want to find.

Technique 1: Recognizing Standard Form

First, make sure your equation is in standard form. For example, if you have:

$$2x^2 + 5x - 3 = 0$$

You can easily see that:

• $a = 2$
• $b = 5$
• $c = -3$

Technique 2: Rearranging Equations

Sometimes, you might find a quadratic equation written differently. For example:

$$x^2 + 4 = 3x$$

To find the coefficients, you need to rearrange it into standard form:

$$x^2 - 3x + 4 = 0$$

Now, you can easily spot:

• $a = 1$
• $b = -3$
• $c = 4$

Technique 3: Using Factorization

If you see an equation that looks like this:

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

You need to expand it to find the coefficients:

$$y = x^2 - 3x + 2$$

Now, you can see:

• $a = 1$
• $b = -3$
• $c = 2$

By practicing these techniques, finding coefficients in quadratic equations will become super easy!