For which value of x does g(x) reach its mini… | GMAT Sprint

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PS · Problem Solving

sub-505

Functions

For which value of $x$ does $g(x)$ reach its minimum, given that $g(x) = x^2 + 4x + 4$ for all real numbers $x$ ?

Answer Choices

Correct answer marked below

-2

Correct

-3

-4

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Explanation

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Official Explanation

Official

To find the maximum of g(x) = x^2 + 4x + 4, we can rewrite it as g(x) = (x + 2)^2.

Evaluating at the options:

A. 1 gives g(1) = (1 + 2)^2 = 3^2 = 9.

B. 0 gives g(0) = (0 + 2)^2 = 2^2 = 4.…

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Comments

NainaaSep 2, 2024

got this wrong on my practice

AmaanApr 9, 2024

Good question

IarinaSep 3

thanks, this one was quick. vertex form makes it obvious

ZachariahJun 8

wait why is it not 0? i keep thinking minimum means where x is smallest

KamilJun 13

nah the minimum is the lowest point of the parabola, not the smallest x value. plug in a couple of the choices and you'll see which one gives the smallest g(x)

HarikaJun 9

ohhh right, it's the y-value that's minimized, not x. got it thanks

HiteshwarApr 24

is this really sub-505? felt a little tricky until i remembered the vertex formula

AfnanJul 27

easy points if you spot that the expression factors. don't overthink it

What this question tests

What it tests

Your ability to evaluate and compose functions, including unusual defined operations.

Common trap

Applying function operations in the wrong order or ignoring domain restrictions.

For which value of xxx does g(x)g(x)g(x) reach its minimum, given that g(x)=x2+4x+4g(x) = x^2 + 4x + 4g(x)=x2+4x+4 for all real numbers xxx?