How do you convert intercept form to standard form of a quadratic equation?

To convert an intercept form of a quadratic equation to standard form, you start with the intercept form, which is given by:

y = a(x – p)(x – q)

Here, p and q are the x-intercepts of the quadratic, and a is a coefficient that affects the width and direction of the parabola.

Follow these steps to convert it:

1. Expand the factors: Distribute the expression:
2. Start by multiplying the two binomials:

(x – p)(x – q) = x² – (p + q)x + pq

3. Multiply by ‘a’: Now, multiply the entire expression by ‘a’:

y = a(x² – (p + q)x + pq) = ax² – a(p + q)x + apq

4. Reorganize into standard form: The standard form of a quadratic is:

y = Ax² + Bx + C

Therefore, you can now see your equation is:

y = ax² + (-a(p + q))x + apq

In this form, A = a, B = -a(p + q), and C = apq. That’s how you successfully convert the intercept form of a quadratic equation to its standard form!