What is the y-value of the vertex of the function f(x) = –(x + 8)(x – 14)?

y-value of the vertex of the given function is 121.

Step-by-step explanation:

Given function f(x) = -( x + 8 )( x - 14 )

We need to find y-coordinate of the vertex of the function.

let, y = -( x + 8 )( x - 14 )

y = -( x( x - 14 ) + 8( x - 14 ) )

y = -( x² - 14x + 8x - 112 )

y = -( x² - 6x - 112 )

Clearly this equation is of parabola. So, now we use completing the square method to write this equation in standard equation of parabola.

y = -( x² - 6x + 3² - 3² - 112 )

y = -( x -  3 )² - ( -9 - 112 )

y = -( x -  3 )² + 121

y - 121 = -( x -  3 )²

( x -  3 )² = -( y - 121 )

y-coordinate of the  vertex of the parabola is 121.

Therefore, y-value of the vertex of the given function is 121.

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