# Which of the following is the vertex of the quadratic equation y = 6x^2 – 24x + 32?

Sep 4, 2016

Vertex$\to \left(x , y\right) = \left(2 , 8\right)$

#### Explanation:

The method used is part way to completing the square plus anticipating part of the final stage.

Write as:$\text{ } y = 6 \left({x}^{2} - \frac{24}{6} x\right) + 32$

${x}_{\text{vertex}} = \left(- \frac{1}{2}\right) \times \left(- \frac{24}{6}\right) = 2$
Thus by substitution we have:

${y}_{\text{vertex}} = 6 {\left(2\right)}^{2} - 24 \left(2\right) + 32$

${y}_{\text{vertex}} = 8$