Question

What is the vertex of `y= x^2+4x + 1`?

Answer 1

`P_("vertex")=(-2,-3)`

Explanation:

Given: `color(brown)(y=x^2+4x+1) ............................(1)`

Let point of vertex be `P_("vertex")`

Extract the 4 from `4x`

Do the following to it:

`-1/2xx4=-2`

`x_("vertex")=color(blue)(-2)............................(2)`
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Substitute (2) into equation (1) to find `y_("vertex")`

`color(brown)(y_("vertex")=color(blue)((-2))^2+4color(blue)((-2))+1)`

`y_("vertex")= 4-8+1 =-3`
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