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

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Answer 1 · 2016-03-30T14:59:52

Vertex $" "->" "(x,y)" "->" "(3,-20)$

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: $" "y=3x^2-18x+7$

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

Write as: $" "y=3(x^2-18/3x)+7$

Apply $(-1/2)xx(-18/3) = +9/3=3$

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

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Compare this to the graph
Tony B
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$color(blue)("Determine "y_("vertex"))$

Substitute $x=3$ into the original equation

$color(brown)(y=3x^2-18x+7)" "->" "y=3(3)^2-18(3)+7$

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

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

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