Test
Systems with a quadratic equation
Dynamic line-parabola systems, intersections, substitution and contextual modelling.
Time left: 00:00:00
Sample questions
- Solve y = x² and y = ___.
- Solve y = x² and y = ___x.
- Does (___, ___) satisfy y = x² and y = ___?
- How many solutions does y = x² and y = ___ have?
- Solve x + y = ___ and xy = ___. Give the pair where x < y.
Systems with a quadratic equation
For a system containing a linear and a quadratic equation, express one variable from the linear equation and substitute it into the quadratic equation. This reduces the system to one quadratic equation.
Geometric meaning
Solutions are intersection points of the graphs, so there may be zero, one or two. For each value of one variable, calculate its corresponding second value separately. Check every ordered pair in both original equations and do not mix values belonging to different pairs.
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