Express ${{x}^{2}}+2x-2$ in the form ${{(x+a)}^{2}}+b$.[2] Sketch the graph of \(y={{x}^{2}}+2x-

Question

Express ${{x}^{2}}+2x-2$ in the form ${{(x+a)}^{2}}+b$.[2] Sketch the graph of $y={{x}^{2}}+2x-2$ on suitable axes. Indicate clearly the coordinates of the points where the graph crosses the axes and the minimum point on the curve.[3] Explain how your graph shows that there is more than one solution of the equation ${{x}^{2}}+2x-2=0$.[1]

Accepted Answer

(a) $(x+1)^2-3$. (b) Minimum $(-1,-3)$; intercepts $(-1\pm\sqrt3,0)$ and $(0,-2)$. (c) Two distinct crossings give two real roots.

2023 AISS S3 EM P1 Q9

2023 AISS S3 EM P1 Q9

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