Question

What is the the vertex of `y=(x - 8)^2 + 20x+70`?

Answer 1

`"the vertex is at: "(x, y)-> (-2,color(white)(.)131)`

Explanation:

Expanding the bracket:
`color(blue)(y=color(brown)((x^2-16x+64 ))+20x+70`

Collecting like termes

`y=x^2+4x+135.....................................(1)`

Consider the `=4x` term

`color(green)(x_("vertex") = color(black)((-1/2)xx(+4)=)-2)...............(2)`

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`color(brown)("Note that the equation must be in the form")`
`color(brown)(y=a(x^2+b/ax) + c ". In your case " a=1 )`

`color(brown)("so you end up with "color(green)( x_("vertex")= (-1/2)xx(b/a)))`
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Substitute (2) into (1) giving:

`y=(-2)^2+4(-2)+135`

`y=4-8+135`

`y=131`

`color(blue)("So the vertex is at: "(x, y)-> (-2,131))`