"A quadratic equation is any equation that can be rearranged in standard form..."
Solving quadratic equations involves finding the value of an unknown variable in an equation with a second-degree polynomial.
Quadratic Formula: How to use the quadratic formula, which provides a general formula for solving quadratic equations of the form ax²+bx+c=0.
Completing the Square: A technique for transforming a quadratic equation into a form that makes it easier to solve using the quadratic formula.
Factoring: Factoring quadratic equations into two binomial factors can help solve for the roots of a quadratic equation.
Discerning Roots (Real, Imaginary, and Complex): How to distinguish and calculate real, imaginary, and complex roots using the quadratic formula.
Vertex Form of Quadratic Equations: A technique for rewriting quadratic equations in the "vertex form" or the "standard form" to help solve equations, find the vertex or roots of a quadratic equation.
Graphing Quadratic Functions: Understanding the shape and features of parabolic graphs, including the vertex, axis of symmetry, minimum or maximum value, and intercepts.
Word problem applications: How to construct, translate and solve real-world problems using quadratic equations.
Quadratic Applications in Physics and Geometry: Using quadratic equations to solve various problems in physics, such as projectile motion, and geometry, such as finding the area of a quadrilateral.
Practice Problems: Work through various example problems of different types of quadratic equations, to better understand how to apply various techniques learned.
Factoring: Factoring is the process of rewriting a quadratic equation in terms of its factors. This method is only applicable when the quadratic expression is factorizable i.e. when its discriminant is perfect square.
Completing the square: Completing the square is a method used to solve quadratic equations by adding and subtracting a suitable constant to the given quadratic equation to make the LHS a perfect square.
Square root method: The square root method is used to solve quadratic equations in which the quadratic expression is in the form of the square of a single variable.
Quadratic Formula method: The quadratic formula is a formula that gives the two solutions of any quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.
Graphing method: Graphing a quadratic equation can provide a visual solution and graphical interpretations of the quadratic equation.
Newton-Raphson method: It is an interactive method that makes use of derivatives to approximate the root of the quadratic equation.
Matrix method: It is a method used to solve a system of quadratic equations.
Synthetic division method: This method is used to find the zeros of a polynomial using long division.
Factoring with a calculator: Factoring can be done by use of advanced calculators.
Trial and error method: In this method, candidates for a solution are tried in succession until the correct one is found.
"x represents an unknown value..."
"The numbers a, b, and c are the coefficients of the equation..."
"A quadratic equation has at most two solutions."
"The values of x that satisfy the equation are called solutions..."
"The values of x that satisfy the equation are called roots or zeros..."
"If there is only one solution, one says that it is a double root."
"If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other."
"A quadratic equation always has two roots..."
"A quadratic equation can be factored into an equivalent equation..."
"Solutions to problems that can be expressed in terms of quadratic equations were known as early as 2000 BC."
"Because the quadratic equation involves only one unknown, it is called 'univariate'."
"The quadratic equation is a polynomial equation."
"It is a second-degree polynomial equation, since the greatest power is two."
"The quadratic formula expresses the solutions in terms of a, b, and c."
"Completing the square is one of several ways for deriving the formula."
"...can be rearranged in standard form as ax^2 + bx + c = 0..."
"...a, b, and c represent known numbers, where a ≠ 0."
"...may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term."
"...two complex solutions that are complex conjugates of each other." Quote: "A quadratic equation is any equation that can be rearranged in standard form as ax^2 + bx + c = 0..." Quote: "The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side." Quote: "A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two." Quote: "A quadratic equation can be factored into an equivalent equation where r and s are the solutions for x." Quote: "The quadratic formula expresses the solutions in terms of a, b, and c." Quote: "Solutions to problems that can be expressed in terms of quadratic equations were known as early as 2000 BC." Quote: "Because the quadratic equation involves only one unknown, it is called "univariate"." Quote: "The quadratic equation contains only powers of x that are non-negative integers, and therefore it is a polynomial equation." Quote: "It is a second-degree polynomial equation since the greatest power is two."