If the roots of a quadratic equation are 3 and -2, what is the equation in standard form?

To find the standard form of a quadratic equation based on its roots, we can use the fact that if the roots are given, the equation can be expressed in factored form as ( y = (x - r_1)(x - r_2) ), where ( r_1 ) and ( r_2 ) are the roots. In this case, the roots of the quadratic equation are 3 and -2.

Substituting the roots into the factored form gives:

[

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

]

Now, to convert this into standard form, we need to expand the factors:

1. Distribute ( x ) into ( (x - 3) ):

• ( x \cdot (x + 2) = x^2 + 2x )

2. Then multiply ( -3 ) into ( (x + 2) ):

• ( -3 \cdot (x + 2) = -3x - 6 )

3. Now, combine all terms:

• ( y = x^2 + 2x - 3x - 6 )

• Combine