Quadratic Formula

Front

Solutions of a quadratic equation are also called

Back

All of the above (roots, x-intercepts, zeros)

Front

Why are quadratic equations set equal to zero?

Back

Because we are trying to find the x-intercepts and that happens when y=0.

Front

If there is one solution, the discriminant is . . .

Back

zero

Front

If there are no real solutions, the discriminant is

Back

a negative number

Front

The first step in solving quadratic equations is to . . .

Back

write the equation in standard form.

Front

What is the standard form of a quadratic equation?

Back

ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the discriminant tell us about the solutions of a quadratic equation?

Back

It indicates the nature of the roots: positive means two real solutions, zero means one real solution, and negative means no real solutions.

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a) for the equation ax² + bx + c = 0.

Front

What is a perfect square trinomial?

Back

A trinomial that can be expressed as the square of a binomial, e.g., (x + a)² = x² + 2ax + a².

Front

How can you determine if a quadratic equation can be factored easily?

Back

By checking if the discriminant is a perfect square.