Consider the equation of parabola f(x)= -(x+7)²-10. What is the x− coordinate of the vertex?

Answer 1

This equation is written in vertex form : f(x)=a(x-h)2 + k, so the vertex is (h,k).

The vertex is (-7, -10) so the x-coordinate is -7.

Another way to solve is by graphing and identifying the vertex from the graph.

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Answer 2

the x coordinate of the vertex is -7

the vertex is (-7,-10)= the maximum point

the given downward opening parabola is already in vertex form f(x) = a(x-h)^2 +k where (h,k) is the vertex and a<0. you can read off the vertex the way it's written. y coordinate of the vertex is k=-10, x coordinate is h =-7

or another method is:

y=-(x+7)^2 -10

the vertex is the maximum point

take the derivative, set =0

y = -x^2 -14x -49 -10

y' = -2x -14 = 0

x = 14/-2 = -7 = x coordinate of the vertex