User:
• Matrices
• Algebra
• Geometry
• Graphs and functions
• Trigonometry
• Coordinate geometry
• Combinatorics
 Suma y resta Producto por escalar Producto Inversa
 Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
 2-D Shapes Areas Pythagorean Theorem Distances
 Graphs Definition of slope Positive or negative slope Determine slope of a line Equation of a line Equation of a line (from graph) Quadratic function Parallel, coincident and intersecting lines Asymptotes Limits Distances Continuity and discontinuities
 Sine Cosine Tangent Cosecant Secant Cotangent Trigonometric identities Law of cosines Law of sines
 Equations of a straight line Parallel, coincident and intersecting lines Distances Angles in space Inner product

 Quadratic Equations Equations in Quadratic Form Some equations are not quadratic equations, but are in the same form. To solve equations such as that, make a substitution, solve for the new variable, and then solve for the original variable $\fs2x^4-5x^2+4\;=\;0\;\Rightarrow\;\;y=x^2$$\fs2y^2-5y+4\;=\;0\;\Rightarrow\;y=\frac{5\pm\sqrt{(-5)^2-4\;1\;4}}{2\;1}\;\Rightarrow\;y=\frac{5\pm\sqrt{25-16}}{2}\;\Rightarrow\;y=\frac{5\pm3}{2}$$\fs2y_1=\frac{5+3}{2}=\frac{8}{2}=4\;\;\;\;y_2=\frac{5-3}{2}=\frac{1}{2}=1$These give$\fs2x^2\;=\;y_1\;\Rightarrow\;\;x^2\;=\;4\;\Rightarrow\;\;x\;=\;\pm2$ $x^2\;=\;y_2\;\Rightarrow\;x^2\;=\;1\;\Rightarrow\;\;x\;=\;\pm1\;\;\;$ Solve $\fs1x^4-90x^2+729\;=\;0$ No solution One solution x= Two solutions x1= x2= Three solutions x1= x2= x3= Four solutions x1= x2= x3= x4=