Solving Quadratics

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 discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant indicates the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if zero, there is one real root (a repeated root); if negative, there are no real roots (two complex roots).

Front

Solve: x² - 5x + 6 = 0

Back

x = 2, 3

Front

What is the vertex of a parabola represented by the quadratic equation y = ax² + bx + c?

Back

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

Front

Solve: 3x² + 12x + 12 = 0

Back

x = -2, -2 (double root)

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

Front

What is the factored form of a quadratic equation?

Back

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

Front

Solve: x² + 4x - 5 = 0

Back

x = 1, -5

Front

What is the axis of symmetry in a quadratic function?

Back

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

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.