Draw the graph of $y = x^{2} - 4 x + 6$ and show that it does not have real roots.

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Solution

To draw the graph, consider the following table

$\begin{matrix} x & 0 & 1 & - 1 & 2 y & 6 & 3 & 11 & 12 \end{matrix}$

Scale: x-axis 1 cm = 2 units; y-axis 1 cm = 2 units

The graph lies above the x- axis. Since it is not intersecting the x- axis, the roots of the graph are not real.

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y = x^{2} + 3 x + 2

x^{2} + 2 x + 4 = 0

x^{2} - 4 x + {log}_{\frac{1}{2}} A = 0

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x^{2} - 4 x + l o g_{\frac{1}{2}} a = 0

y = x^{2} - x - 2

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