Factoring Quadratic Polynomials (a=1)

Front

Define a quadratic polynomial.

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic polynomial?

Back

The standard form of a quadratic polynomial is written as f(x) = ax² + bx + c.

Front

What does it mean to factor a quadratic polynomial?

Back

Factoring a quadratic polynomial means expressing it as a product of two binomials.

Front

What is the factored form of y² + 2y - 24?

Back

(y + 6)(y - 4)

Front

How do you find the factors of a quadratic polynomial?

Back

To find the factors, look for two numbers that multiply to 'c' and add to 'b' in the polynomial ax² + bx + c.

Front

What is the significance of the leading coefficient in a quadratic polynomial?

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the vertex of a parabola represented by a quadratic polynomial?

Back

The vertex is the highest or lowest point of the parabola, found at the point (-b/2a, f(-b/2a)).

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 are the roots of a quadratic polynomial?

Back

The roots are the values of x that make the polynomial equal to zero.

Front

What does it mean if a quadratic polynomial has no real roots?

Back

It means the discriminant (b² - 4ac) is less than zero, indicating the parabola does not intersect the x-axis.