Articles

\(a_n \ = \ a_1 \ + \ d \ (n \ – \  1)\)

• \(a_1 =\) The first term
• \(d =\) The common difference between terms
• \(n =\) The term poistion

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In math, logarithm problems are solved using the properties of the functions that make up logarithms. In basic math, we learned a lot of properties, like commutative, associative, and distributive, that can be used in algebra. When it comes to logarithmic functions, there are five main things to know.
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Consider: \(log_b \ x \ = \ y\):

• Rewrite the exponential expression "\(x\)" as a power of "\(b\)": \(b^y \ = \ x\)
• Use what you know about powers to figure out what \(y\) is by asking, "To what exponent should \(y\) be raised to get \(x\)?"

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If you realize that logarithms are just another way to write out exponential equations, it becomes much easier to solve a logarithm. Once you change the logarithm into a form that is easier to understand, you should be able to solve it the same way you would solve an ordinary exponential equation.
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Matrix's inverse is another matrix that gives the multiplicative identity when multiplied by the given Matrix. The inverse of a matrix \(A\) is \(A^{-1}\) and \(A.A^{-1} \ = \ A^{-1}.A \ = \ I\) (\(I\) is the identity matrix). An invertible matrix is one whose determinant is not zero and for which the inverse matrix can be calculated.
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The determinant of a matrix is a unique number that is only defined for square matrices (matrices with the same number of rows and columns). A determinant is used in calculus and other algebra-related matrices. It is a real number representing the matrix and can be used to solve a system of linear equations and find the inverse of a matrix.
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The basic operations on a matrix are addition, subtraction, and multiplication. For matrices to be added or subtracted, they must be in the same order. For matrices to be multiplied, the number of columns in the first Matrix must equal the number of rows in the second Matrix.
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A quadratic inequality has two roots, or x-intercepts because it has an \(x^2\) term. You get a parabola when you plot this inequality on a coordinate plane. Finding the values of \(x\) that make the inequality true is what it means to solve an inequality. By drawing the inequality, you can show these solutions in algebra or on a number line or coordinate plane.
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- Discriminant determines the number of solutions for the given quadratic equation.
- The discriminant, is the part of the quadratic formula under the square root.
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
- If  discriminant is positive, there are 2 solutions, if it’s zero, there is one solution, and if it’s negative, there is no solution for the quadratic function.
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Putting quadratic functions on a coordinate plane is the process of quadratic graphing functions.
This guide will teach you how to draw graphs of quadratic functions. Both general form and vertex form can be used to graph quadratic functions.
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