Mastering Quadratic Equations: The Basics And Different Forms

Quadratic Parent Equation

y=x^3

The quadratic parent equation is y = x². This is the simplest quadratic equation that describes a parabola which opens upwards. The graph of this equation is a curve that starts at the origin (0,0), and as x becomes positive or negative, the curve increases (x > 0) or decreases (x < 0) rapidly. The vertex of this parabola is at the origin. A quadratic equation is defined as an equation of second degree, which means that the highest power of the variable is 2. Quadratic equations can be written in different forms, such as vertex form, standard form, and factored form. The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) represents the vertex of the parabola, and a is a scaling factor. The vertex form can be transformed into standard form, which is y = ax² + bx + c, where a, b, and c are constants. Standard form is the most common way to write quadratic equations, and it is useful to find the x-intercepts (zeros) of the parabola. Factored form is written as y = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation, or the values of x where y = 0. All quadratic equations are related to the quadratic parent equation y = x², because they are transformations of this basic equation. To graph any quadratic equation, we can start with the parent equation and apply the transformations of translation, reflection, stretching or shrinking, and vertical shift.

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