Brian McLogan
Finding the Zeros and Multiplicity of a Quadratic Function
👉 Learn how to find all the zeros of a polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values...
Brian McLogan
Given One Zero or Factor Find the Remaining Zeros
👉 Learn how to find all the zeros of a polynomial given one rational zero. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a...
Brian McLogan
How to take the derivative of an equation implicitly
👉 Learn how to find the derivative of an implicit function. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative of a...
Brian McLogan
Evaluate the limit at a hole by factoring
👉 Learn how to evaluate the limit of a function involving rational expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The...
Brian McLogan
How to find the domain of a rational function - domain and range
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...
Brian McLogan
Use baby numbers to evaluate the right hand limit of a rational function
👉 Learn how to evaluate the limit of a function involving rational expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The...
Brian McLogan
Use the product rule to take the derivative of an exponential equation
👉 Learn how to find the derivative of exponential and logarithmic expressions. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the...
Brian McLogan
Learn how to write the domain of a rational function using interval notation
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...
Brian McLogan
Evaluate left hand limits algebraically of a rational function
👉 Learn how to evaluate the limit of a function involving rational expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The...
Brian McLogan
How to find all the roots of a polynomial by factoring
👉 Learn how to find all the zeros of a polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values...
Brian McLogan
Given three real zeros, learn how to write the equation of a polynomial
👉 Learn how to write the equation of a polynomial when given rational zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...
Brian McLogan
Applying equality property of logarithms to solve by factoring, log4 (x^2 -4)=log4 (-x+2)
👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the...
Brian McLogan
Domain of a rational function by factoring
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...
Brian McLogan
Using zero product property to solve for tangent with a multiple angle
👉 Learn how to solve trigonometric equations using the zero product property. The zero product property states that when the product of two quantities is equal to 0, then either of the quantities is zero. When solving factored...
Brian McLogan
Solving a trigonometric equation by factoring
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a...
Brian McLogan
Solve a quadratic by applying the square root method
👉Learn how to solve quadratic equations using the square root method. It is important to understand that not all quadratics have to be solved using factoring or quadratic formula. When we only have one variable but it is squared we can...
Brian McLogan
Given a list of three zeros find the factors of the polynomial
👉 Learn how to write the equation of a polynomial when given rational zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...
Brian McLogan
How to use the pythagorean identity to simplify an expression
👉 Learn how to simplify rational identities involving addition and subtraction. To simplify rational identities involving addition and subtraction, first, we find the LCM of the denominators which most time is the product of the terms in...
Brian McLogan
Learn to find the zeros of a quadratic using the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a...
Brian McLogan
Apply the equality property of logarithms to solve an equation, log13 (x^2 -4)=log13 (3x)
👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the...
Brian McLogan
Learn how to solve a quadratic equation using the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a...
Brian McLogan
What is the formula for a perfect square trinomial and how does the discriminant fit in
👉 Learn all about the discriminant of quadratic equations. A quadratic equation is an equation whose highest power on its variable(s) is 2. The discriminant of a quadratic equation is a formula which is used to determine the type of...
Brian McLogan
How do we solve quadratic equations
👉Learn how to solve quadratic functions. Quadratic equations are equations whose highest power in the variable(s) is 2. They are of the form y = ax^2 + bx + c. There are various techniques which can be applied in solving quadratic...
Brian McLogan
Solve a trigonometric function with sine on both sides
👉 Learn how to solve trigonometric equations by factoring out the GCF. When solving trigonometric equations involving the multiples of the same trigonometric function. It is very useful to collect similar trigonometric functions together...