A function is defined by f(x) = x^2 + 4x – 5. What is the minimum valu

Question

A function is defined by  f(x) = x^2 + 4x – 5 . What is the minimum value of  f(x) ?

(A) 1

(B) 0

(C) –5

(D) –8

(E) –9

CrackverbalGMAT · Accepted Answer

The function defined in the question is a quadratic function with a positive co-efficient for  x^2 . There are two methods which can be adopted to solve this question. 
Let’s discuss both of them in detail.

For a quadratic function of the form a x^2  + bx + c where a>0, the minimum value of the function is given by  \frac{4ac – b^2}{4a} .

Comparing the function given in the question with the standard form, we have,

a = 1, b = 4 and c = -5.

Substituting these values in the expression above, we have,

Minimum value of f(x) =  \frac{4 * 1 * (-5) – (4)^2}{4*1}  =  \frac{- 20 – 16}{4}  = -9.

For a quadratic function of the form a x^2  + bx + c where a>0, the minimum value of the function occurs at x =  \frac{-b}{2a} .

This means, for the given function, the minimum value of the function occurs at x =  \frac{-4}{2}  = -2.

Substituting this value in the function, we have f(-2) = 4 – 8 – 5 = -9.
Therefore, the minimum value of the given function is -9. The correct answer option is E.

Hope this helps!

EgmatQuantExpert · Answer

Solution 
  Given:  
 •  f(x) = x^2 + 4x – 5

To find:  
 • The minimum value of f(x)

Approach and Working Out:   
 • f(x) =  x^2 + 4x – 5 = (x + 2)^2 – 9 
• The minimum value of  (x + 2)^2 = 0 
• Therefore the minimum value of f(x) = 0 – 9 = -9

Hence, the correct answer is Option E.

Answer: E

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-Algebra-e1533292163516.png

Mohammadmo · Answer

If you put -2, instead of X,the function will be the lowest amount.
Option (E)

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Kinshook · Answer

Given:  A function is defined by  f(x) = x^2 + 4x – 5 .

Asked:  What is the minimum value of  f(x) ?

f(x) = x^2 + 4x – 5 = (x+2)^2 -9 . 
Since  (x+2)^2 =0  for f(x) to be minimum
Minimum value of f(x) = -9

IMO E

manpaslop · Answer

f(x)=x^2 +4x-5
f'(x)=2x+4

When f'(x)=0, we have the single minimum. f'(x)=0 when x=-2. Then f(-2)=-9.

barsec · Answer

This problem can be easily solved by taking the derivative of the parabolic formula. In this case we are looking for when the slope is equal to 0, slope at a point on a graph is equal to the first derivative on the function in question.

Function: f(x)=x^2+4x–5
Derivative: f'(x) = 2x+4

Solve for when the slope is equal to 0:
 0=2x+4
 X=-2
Plug point back into original function to find corresponding minimum value:
 f(-2)=-9

BrushMyQuant · Answer

Given that  f(x) = x^2 + 4x – 5  and we need to find the minimum value of  f(x)

f(x) = x^2 + 4x – 5  =  x^2 + 4x + 4 - 4 – 5  =  x^2 + 2*2x + 2^2 -9  =  (x+2)^2 - 9

Now, we know that a Square of a number is always  \geq  0
=> Minimum value of  (x+2)^2  = 0
=> Minimum vale of f(x) =  (x+2)^2 - 9  = 0-9 = -9

So,  Answer will be E 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

himssss29 · Answer

Step 1: Find x at vertex using −b/2a

x=−b/2a =-4/2(1)= −2

Step 2: Substitute x = -2 into f(x)

f(−2)=(−2)^2 +4(−2)−5=4−8−5=−9

Answer: (E) –9

Important Concept to Remember-

Where to use -b/2a=

Coefficient sign  
  Parabola shape  
  Max exists?  
  Min exists?  
 
   Negative  
 Downward (∩) 
 ✅ Yes — at vertex 
 ❌ No (goes to −∞) 
 
   Positive  
 Upward (∪) 
 ❌ No (goes to +∞) 
 ✅ Yes — at vertex (if in valid domain)

vrinda6 · Answer

Bunuel  are there any other alternate questions like these? Can you help?

Bunuel · Answer

Check similar questions block at the bottom of the page. Hope it helps.

A function is defined by f(x) = x^2 + 4x – 5. What is the minimum valu

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Coefficient sign	Parabola shape	Max exists?	Min exists?
Negative	Downward (∩)	✅ Yes — at vertex	❌ No (goes to −∞)
Positive	Upward (∪)	❌ No (goes to +∞)	✅ Yes — at vertex (if in valid domain)

GMAT Problem Solving (PS) Questions

A function is defined by f(x) = x^2 + 4x – 5. What is the minimum valu

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