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Vertex of a Parabola

"In order to graph a parabola, we need to find several pieces of information, including the vertex. One way to find the vertex of a parabola is to turn the standard form of the quadratic equation into ...

Velocity and Acceleration

"If position is given by a function p(x), then the velocity is the first derivative of that function, and the acceleration is the second derivative. By using differential equations with either velocit ...

Vectors and Planes

"An important calculation when dealing with vectors and planes, is being able to find a vector normal to a plane through a specific point. There are methods for finding the normal or perpendicular vec ...

Vector Equation of a Line

"We can use vectors to create the vector equation of a line. In order to create the vector equation of a line we use the position vector of a point on the line and the direction vector of the line. In ...

Vector Dot Product

"An operation used frequently on vectors is the vector dot product, sometimes known as the scalar product. The vector dot product is an operation on vectors that takes two vectors and produces a scala ...

Using Trigonometric Identities

"When simplifying problems that have reciprocal trig functions, start by substituting in the identities for each. If possible, write tangent in terms of sine and cosine. Use algebra to eliminate any ...

Using the Sine and Cosine Addition Formulas to Prove Identities

":Applying the cosine addition and sine addition formulas proves the cofunction, add pi, and supplementary angle identities. Using the formulas, we see that sin(pi/2-x) = cos(x), cos(pi/2-x) = sin(x) ...

Kite Properties

"Knowing the properties of a kite will help when solving problems with missing sides and angles. Kite properties include (1) two pairs of consecutive, congruent sides, (2) congruent non-vertex angles ...

Using the Second Derivative Test

"Some optimization problems can be solved by use of the second derivative test. If the second derivative is always positive, the function will have a relative minimum somewhere. If it is always negati ...

Using the First Derivative Test

"Some optimization problems use the first derivative test to find an absolute minimum or maximum. Using the first derivative test requires the derivative of the function to be always negative on one s ...

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