For what value of x between -4 and 4 , inclusive, is the value of x^2-10 x+16 the greatest?

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GMAT Panda · Accepted Answer

-4 We first name the function based on the given expression. f(x)=x^2-10 x+16 We notice that the squared term has a positive coefficient, so the function values will be larger at the ends of the interval. x=-4 or x=4 We then find the value of the function at each endpoint using grouping to simplify the sums. f(-4)=(-4)^2-10(-4)+16=16+40+16 =40+(16+16)=40+32=72 f(4)=4^2-104+16=16-40+16 =(16+16)-40=32-40=-8 We compare these results to see which is larger. 72>-8

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$We first name the function based on the given expression.$	$f (x) = x^{2} - 10 \times x + 16$
$We notice that the squared term has a positive coefficient, so the function values will be larger at the ends of the interval.$	$x = - 4 or x = 4$
$We then find the value of the function at each endpoint using grouping to simplify the sums.$	$f (- 4) = (- 4)^{2} - 10 \times (- 4) + 16 = 16 + 40 + 16 = 40 + (16 + 16) = 40 + 32 = 72 f (4) = 4^{2} - 10 \times 4 + 16 = 16 - 40 + 16 = (16 + 16) - 40 = 32 - 40 = - 8$
$We compare these results to see which is larger.$	$72 > - 8$

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