Question

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

Answer 1

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

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:`" "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

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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)`