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Enter the coordinates of the vertex of the function f(x) = x2 + 4x - 7

Enter The Coordinates Of The Vertex Of The Function Fx X2 4x 7 class=

Sagot :

Given the equation of the function:

[tex]f(x)=x^2+4x-7[/tex]

The given function represents a parabola

We will make a complete square to find the coordinates of the vertex

The coefficient of x = 4

Half the coefficient of x = 2

Square it give = 4

So, we will add and subtract 4

[tex]\begin{gathered} f(x)=x^2+4x+4-4-7 \\ f(x)=(x^2+4x+4)-11 \\ f(x)=(x+2)^2-11 \end{gathered}[/tex]

Compare the last equation with the vertex form of the parabola

[tex]f(x)=(x-h)^2+k[/tex]

So, h = -2, k = -11

So, the answer will be the coordinates of the vertex = (-2, -11)

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