The curve \(y=x^2-2x-5\) is drawn on the grid. Use the graph to find the two values of \(x\) when \(y=3\).
Question 1 Report
The curve \(y=x^2-2x-5\) is drawn on the grid.
Use the graph to find the two values of \(x\) when \(y=3\).
Answer Details
Using a graph to solve \(x^2 - 2x - 5 = 3\) means drawing the horizontal line \(y = 3\) across the grid and reading the \(x\)-coordinates of the two points where it cuts the curve. The intersections are exactly the values of \(x\) that make the curve's \(y\)-value equal to \(3\).
The algebra confirms the readings. Setting the expression equal to \(3\):
\[ x^2 - 2x - 5 = 3 \] \[ x^2 - 2x - 8 = 0 \] \[ (x - 4)(x + 2) = 0 \]So the solutions are
\(x = 4\) [B1] and \(x = -2\) [B1]
Check both: at \(x = 4\), \(16 - 8 - 5 = 3\); at \(x = -2\), \(4 + 4 - 5 = 3\).
Two errors are common. The first is solving \(x^2 - 2x - 5 = 0\) instead, which finds where the curve meets the \(x\)-axis rather than where it reaches height \(3\). The second is giving only one root; a horizontal line above the vertex of an upward parabola always crosses it twice, so two values are expected. Notice the two answers are symmetric about \(x = 1\), the line of symmetry of this curve, which is a quick way to check a graphical reading.
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