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raketka [301]
3 years ago
9

Complete the square to determine the maximum or minimum value of the function defined by the expression. x2 + 30x + 21 A) maximu

m value at 15 B) maximum value at 30 C) maximum value at −15 D) minimum value at −204
Mathematics
2 answers:
AveGali [126]3 years ago
8 0
X^2 + 30x + 21
=   ( x + 15)^2 - 225 + 21
= (x + 15)^2 - 204

Its D  minimum at -204
kramer3 years ago
6 0

Answer:

x^2 + 30x + 21=(x+15)^2-204

Option D - minimum value at −204

Step-by-step explanation:

Given : Expression x^2 + 30x + 21

To find : Complete the square to determine the maximum or minimum value of the function defined by the expression?

Solution :  

The general form of quadratic equation is   ax^2+bx+c=0

To convert into complete square the form is a(x+d)^2+e=0

Where, d=\frac{b}{2a} and e=c-\frac{b^2}{4a}

Now, comparing the given equation x^2 + 30x + 21

a=1 , b=30, c=21        

d=\frac{b}{2a}=\frac{30}{2(1)}=15

e=21-\frac{30^2}{4(1)}=21-225=-204

Substitute in a(x+d)^2+e=0

1(x+15)^2+(-204)=0

(x+15)^2-204=0

[tex]x^2 + 30x + 21[/tex]

By Completing the square we get,            

x^2 + 30x + 21=(x+15)^2-204

The minimum value of this is when x+15 = 0 ⇒ x=-15

i.e, (-15+15)^2-204=-204

Therefore, Option D is correct.

Minimum value of the function is at -204.

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