Quadratic #1

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form y = 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 discriminant of a quadratic equation tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How do you find the roots of a quadratic equation?

Back

Roots can be found using factoring, completing the square, or the quadratic formula: x = (-b ± √D) / (2a).

Front

What is factoring in the context of quadratic equations?

Back

Factoring involves rewriting the quadratic equation as a product of two binomials, such as (x - p)(x - q) = 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) in the vertex form y = a(x - h)² + k.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

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

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

How do you determine the number of roots from the discriminant?

Back

Calculate the discriminant (D = b² - 4ac): D > 0 means 2 roots, D = 0 means 1 root, D < 0 means no real roots.