Graphs 7
3 marks · NormalA student is solving the equation graphically.
They draw the curve and the line and find that the graphs intersect at exactly one point.
Explain what this means about the solutions to the equation.
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There is only one real solution to the equation .
Also accept: Only one real solution exists.
Common mistakes: Saying 'only' a solution, not 'real' solution.; Not clarifying the meaning of a single intersection.
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Marking points
B1 · 1 mark · States that the intersection represents solutions to .
B2 · 1 mark · Clearly states there is only one point of intersection (one real solution).
B3 · 1 mark · Explains that if the graphs intersect only once, there is only one real solution to the equation.
Worked solution
The intersection point represents a solution to .
Since there is only one intersection, there is only one real solution.
Thus, the equation has exactly one real root.