Solving Quadratics

Front

What is the equation for the axis of symmetry of a quadratic function?

Back

x = -b/(2a), where a and b are coefficients from the quadratic equation ax^2 + bx + c.

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of the quadratic equation ax² + bx + c = 0.

Front

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

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the discriminant of a quadratic equation tell us?

Back

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

Front

Solve using the quadratic formula: x² - 4x - 5 = 0

Back

x = 5, -1.

Front

What is the vertex of the quadratic function y = 2x² + 4x + 1?

Back

The vertex is (-1, -1).

Front

How do you solve a quadratic equation by factoring?

Back

Set the equation to zero, factor it into two binomials, and set each binomial to zero to find the roots.

Front

What is the vertex form of a quadratic function?

Back

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

Front

Solve using the Square Root Method: x² = 49

Back

x = ±7.