Question 1

What is the quadratic formula?

Accepted Answer

For any equation ax² + bx + c = 0 with a not equal to 0, the solutions are x = (-b ± √(b² - 4ac)) / (2a). The ± means there are usually two answers, one using plus and one using minus.

Question 2

What does the discriminant tell me?

Accepted Answer

The discriminant is b² - 4ac, the part under the square root. If it is positive you get two real solutions, if it is zero you get one repeated solution, and if it is negative the solutions are complex numbers with an i in them.

Question 3

Why does the calculator show a square root instead of a decimal?

Accepted Answer

Algebra 2 and Pre-Calc teachers usually want the exact answer, like (3 + √5) / 2, because a rounded decimal loses information. The calculator shows both the exact simplified form and the decimal so you can match whatever your class expects.

Question 4

Can I use the quadratic formula when a = 0?

Accepted Answer

No. With a = 0 there is no x² term, so the equation is linear and the formula divides by zero. The calculator spots this and solves the linear equation bx + c = 0 instead.

Question 5

How do I know if the quadratic factors?

Accepted Answer

If the discriminant is a perfect square (0, 1, 4, 9, 16, and so on), the roots are rational and the trinomial factors over the integers. The calculator writes out that factored form whenever it exists.

Question 6

Is this calculator free to use for homework?

Accepted Answer

Yes, the calculator is free with no sign-up. If you want the same problem written out as a handwritten page you can turn in, ShowYourWork gives every account 3 free handwritten pages a month.