Solving Quadratic Trinomials a=1

Front

What is a quadratic trinomial?

Back

A quadratic trinomial is a polynomial of the form ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What does the 'a' represent in a quadratic trinomial?

Back

In a quadratic trinomial, 'a' represents the coefficient of the x² term, determining the parabola's direction and width.

Front

How do you factor a quadratic trinomial of the form x² + bx + c?

Back

To factor, find two numbers that multiply to c and add to b, then express as (x + p)(x + q).

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac, which determines the nature of the roots (real and distinct, real and equal, or complex).

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real roots, only complex roots.

Front

How can you determine the vertex of a parabola given a quadratic equation?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the quadratic function.