Mathematics: The axis of symmetry for the function f(x) = −x2 − 10x 16 is x = −5. what are the coordinates of the vertex of the graph? (−5, 41) (−5, 56) (−5, 76) (−5, 91)

The axis of symmetry for the function f(x) = −x2

Nicole3246

05.06.2020

we have

$f(x)=-x^{2} -10x+16$

Convert the function into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-16=-x^{2} -10x$

$f(x)-16=-(x^{2}+10x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-16-25=-(x^{2}+10x+25)$

$f(x)-41=-(x^{2}+10x+25)$

Rewrite as perfect squares

$f(x)-41=-(x+5)^{2}$

$f(x)=-(x+5)^{2}+41$ --------> function in vertex form

the vertex is the point (-5,41)

the axis of symmetry must coincide with the x-coordinate of the vertex

-5=-5 ------> is correct

therefore

the answer is the option

(-5,41)

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