Test: Systems with a quadratic equation

Dynamic line-parabola systems, intersections, substitution and contextual modelling.

Question qty: 10
Duration in minutes: 21
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Sample questions

Solve y = x² and y = c.
What is the main substitution idea for a system containing a linear and a quadratic equation?
How many solutions does y = x² and y = c have?
What do solutions of a two-equation system mean graphically?
Does (x, y) satisfy y = x² and y = y?
A rectangle has perimeter p and area s. Find its side lengths.
Solve x + y = s and xy = p. Give the pair where x < y.
Solve y = x² and y = ax.

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.

Test: Systems with a quadratic equation

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Sample questions

Systems with a quadratic equation

Geometric meaning

Test: Systems with a quadratic equation

Question Nr. 1 out of 10

Question Nr. 2 out of 10

Question Nr. 3 out of 10

Question Nr. 4 out of 10

Question Nr. 5 out of 10

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Question Nr. 9 out of 10

Question Nr. 10 out of 10

Sample questions

Systems with a quadratic equation

Geometric meaning

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