Quadratics Vocab

By Hudson Brock

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Parabola

A parabola is a curve where any point is at an equal distance from

  • a fixed point (the focus), and
  • a fixed straight line (the directrix)
Example is in the picture
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Quadratic

Involving the second and no higher power of an unknown quantity or variable.


Ex,

  • Solve (x + 1)(x – 3) = 0.
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Vertex

Each angular point of a polygon, polyhedron, or other figure.


Example is in picture

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Axis of symmetry

Generally speaking, an object with rotational symmetry, also known in biological contexts as radial symmetry, is an object that looks the same after a certain amount of rotation.


Ex, This is a graph of the parabola y = x2 – 4x + 2 together with its axis of symmetry x = 2.

The axis of symmetry is the red vertical line.

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Maximum value

The y-coordinate of the parabola's vertex (usually represented by k) is also the maximum or minimum value of the quadratic function represented by the parabola.


Ex, The quadratic function f(x) = 9 - x2 has the maximum value of 9.

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Minimum value

The y-coordinate of the parabola's vertex (usually represented by k) is also the maximum or minimum value of the quadratic function represented by the parabola.


Ex, The quadratic function f(x) = 16 + x2 has the minimum value of 16.

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Terms



A Term is either a single number or a variable, or numbers and variables multiplied together.




Ex, An Expression is a group of terms (the terms are separated by + or - signs)


So, now we can say things like "that expression has only two terms", or "the second term is a constant", or even "are you sure the coefficient is really 4?"

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First differences

To find the first differences, subtract successive y-values for equal steps of x-values


Ex,


These are tables

Problem:

x, y

-3, -7

-2, -5

-1, -3

0, -1

1, 1

2, 3

3, 5


Solution:

X, Y

-3, -7

-2, -5

2, -1

-320, -12

1, 1, 2

2, 3, 2

3, 5, 2

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Second differences

  • Difference means the answer of a subtraction equation, such as 4-2=2 the second difference is the second answer to a multi part equation.


Example in picture

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Zeros(roots)

We say that x=r is a root or zero of a polynomial, P(x), if P(r)=0. In other words, x=r is a root or zero of a polynomial if it is a solution to the equation P(x)=0


Ex, Show that if (2+i) is a zero to f(x)=-x2+4x-5 then 2-i is also a zero of the function