Quadratics: Characteristics and Convertion

Front

What is a quadratic equation?

Back

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

Front

What does the 'a' value in a quadratic equation represent?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form (ax² + bx + c) to vertex form (a(x-h)² + k), complete the square.

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of expressing a quadratic equation as a product of its linear factors, such 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 does the discriminant tell you about a quadratic equation?

Back

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

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), which is also the x-coordinate of the vertex.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.