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The calculator can evaluate and simplify algebraic expressions symbolically. For example, entering x^2-4x+4 returns +. The answer is "prettyprinted" by default; that is, displayed as it would be written by hand (e.g. the aforementioned + rather than x^2-4x+4). The TI-89's abilities include:
For example, taking the statement x + 1 = 0, if x is substituted with 1, this implies 1 + 1 = 2 = 0, which is false, which implies that if x + 1 = 0 then x cannot be 1. If x and y are integers, rationals, or real numbers, then xy = 0 implies x = 0 or y = 0. Consider abc = 0. Then, substituting a for x and bc for y, we learn a = 0 or bc = 0.
[3] [4] Expressions can be evaluated or simplified by replacing operations that appear in them with their result. For example, the expression 8 × 2 − 5 {\displaystyle 8\times 2-5} simplifies to 16 − 5 {\displaystyle 16-5} , and evaluates to 11. {\displaystyle 11.}
That is, h is the x-coordinate of the axis of symmetry (i.e. the axis of symmetry has equation x = h), and k is the minimum value (or maximum value, if a < 0) of the quadratic function. One way to see this is to note that the graph of the function f ( x ) = x 2 is a parabola whose vertex is at the origin (0, 0).
f(x) = a 0 + a 1 x + a 2 x 2 + ⋯ + a n x n, where a n ≠ 0 and n ≥ 2 is a continuous non-linear curve. A non-constant polynomial function tends to infinity when the variable increases indefinitely (in absolute value ).
The simplified equation is not entirely equivalent to the original. For when we substitute y = 0 and z = 0 in the last equation, both sides simplify to 0, so we get 0 = 0, a mathematical truth. But the same substitution applied to the original equation results in x/6 + 0/0 = 1, which is mathematically meaningless.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
For example, let a denote a multiplicative generator of the group of units of F 4, the Galois field of order four (thus a and a + 1 are roots of x 2 + x + 1 over F 4. Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits ...