QUADRATIC EQUATIONS

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.

The discriminant indicates the nature of the roots: if > 0, there are two different real solutions; if = 0, there are two equal real solutions; if < 0, there are two imaginary solutions.

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

The axis of symmetry can be found using the formula x = -b / (2a).

The roots are x = -2 and x = -3.

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) where h = -b / (2a) and k is the value of the quadratic function at h.

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

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

A quadratic opens upwards if a > 0 and downwards if a < 0.

The coefficient 'a' determines the direction of the parabola (upward or downward) and affects the width of the parabola.