3 Forms of Quadratics Review

Front

What is the vertex form of a quadratic equation?

Back

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

Front

What does the coefficient 'a' in the vertex form indicate about the parabola?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (larger |a| means narrower, smaller |a| means wider).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

How can you find the vertex of a quadratic 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 are the x-intercepts (or zeros) of a quadratic equation?

Back

The x-intercepts (or zeros) are the points where the graph of the quadratic crosses the x-axis, found by solving the equation y = 0.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is y = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots or x-intercepts.

Front

What is the significance of the discriminant in a quadratic equation?

Back

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

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers.

Front

What is the range of a quadratic function in vertex form?

Back

The range depends on the vertex: if a > 0, range is [k, ∞); if a < 0, range is (-∞, k].

Front

How do you determine if a quadratic has a maximum or minimum value?

Back

If 'a' is positive, the quadratic has a minimum value at the vertex; if 'a' is negative, it has a maximum value at the vertex.