Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem has two parts. Part 1: Given a quadratic equation $7x^2 - 2x + 1 = 0$ with roots $a$ and...
Quadratic EquationsRoots of EquationsGeometric ProgressionSequences and Series
2025/6/30
The problem asks to simplify the expression $\sqrt{48} - \sqrt{75} + \sqrt{12}$ and find the correct...
SimplificationRadicalsSquare Roots
2025/6/30
The problem asks to find the analytical expression of the function $f(x)$ whose graph is shown. The ...
Piecewise FunctionsParabolaLinear EquationsHyperbolaFunction Analysis
2025/6/29
The graph of a function $f(x)$ is given. The function consists of a parabolic arc with vertex $V$, a...
Piecewise FunctionsQuadratic FunctionsLinear FunctionsRational FunctionsFunction Analysis
2025/6/29
The problem is to determine the equation of the function represented by the graph. The graph appears...
FunctionsPiecewise FunctionsQuadratic FunctionsLinear FunctionsHyperbolasGraphing
2025/6/28
The image shows a piecewise function. We need to define the function $f(x)$ based on the graph. The ...
Piecewise FunctionsParabolaLinear FunctionsHyperbolaFunction DefinitionGraph Analysis
2025/6/28
The problem asks to find the general term for the sequence 1, 5, 14, 30, 55, ...
SequencesSeriesPolynomialsSummation
2025/6/27
The problem asks us to find the axis of symmetry and the vertex of the graph of the given quadratic ...
Quadratic FunctionsVertex FormAxis of SymmetryParabola
2025/6/27
The problem asks us to sketch the graphs of the following two quadratic functions: (1) $y = x^2 + 1$...
Quadratic FunctionsParabolasGraphingVertex FormTransformations of Graphs
2025/6/27
Given two complex numbers $Z_a = 1 + \sqrt{3}i$ and $Z_b = 2 - 2i$, we are asked to: I. Convert $Z_a...
Complex NumbersPolar FormDe Moivre's TheoremComplex Number MultiplicationComplex Number DivisionRoots of Complex Numbers
2025/6/27