Express ${{x}^{2}}-9x+12$ in the form ${{(x-h)}^{2}}+k$. State the coordinates of the turning po

Question

Express ${{x}^{2}}-9x+12$ in the form ${{(x-h)}^{2}}+k$. State the coordinates of the turning point. Sketch the graph of $y={{x}^{2}}-9x+12$, showing the intercepts and coordinates of the turning point clearly.

Accepted Answer

(i) $\left(x-\frac92\right)^2-\frac{33}{4}$. (ii) $\left(\frac92,-\frac{33}{4}\right)$. (iii) $y$-intercept $(0,12)$; $x$-intercepts $\left(\frac{9-\sqrt{33}}2,0\right)$ and $\left(\frac{9+\sqrt{33}}2,0\right)$.

IP2U4 Exercise Q19

IP2U4 Exercise Q19

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