# What is the vertex of  y= 3x^2-18x+7?

Mar 30, 2016

Vertex$\text{ "->" "(x,y)" "->" } \left(3 , - 20\right)$

#### Explanation:

There are several way of doing this. I am going to show you a 'sort of' cheat way. In fact it is part of the process for 'completing the square'.

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Given:$\text{ } y = 3 {x}^{2} - 18 x + 7$

color(blue)("Determining "x_("vertex"))

Write as:$\text{ } y = 3 \left({x}^{2} - \frac{18}{3} x\right) + 7$

Apply $\left(- \frac{1}{2}\right) \times \left(- \frac{18}{3}\right) = + \frac{9}{3} = 3$

" "color(blue)(x_("vertex")=3)

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Compare this to the graph

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color(blue)("Determine "y_("vertex"))

Substitute $x = 3$ into the original equation

$\textcolor{b r o w n}{y = 3 {x}^{2} - 18 x + 7} \text{ "->" } y = 3 {\left(3\right)}^{2} - 18 \left(3\right) + 7$

$y = 27 - 54 + 7 = - 20$

" "color(blue)(y_("vertex") = -20)