Write g(x) = 4x² + 88x in vertex form. The function written in vertex form is g(x) = ___ (x +11)² +____.

Solution:

Given g(x) = 4x² + 88x ……………(a)

The vertex form of the parabola is y = a(x - h)² + k.

g(x) = ___ (x +11)² +____

Let the first blank be a and the second blank be k.

g(x) = a(x +11)² + k

Expand (x +11)² as x² + 22x +121

g(x) = a(x² +22x +121) + k

g(x) = ax² + 22ax +121a + k ….…….(b)

Equate eq(a) and eq(b) We get,

4x² + 88x = ax² + 22ax +121a + k

Compare the coefficients of x on both sides

a=4 and 22a= 88 ; 121a + k = 0

121(4) = -k

k = -484

g(x) =4x²+88x =4(x+ 11)² - 484 

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Write g(x) = 4x² + 88x in vertex form. The function written in vertex form is g(x) = ___ (x +11)² +____.

Summary:

If g(x) = 4x² + 88x is in vertex form. The function written in vertex form is g(x) = 4(x +11)² -484.