The maximum or minimum of a quadratic function occurs at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mstyle></math> . If <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> is negative, the maximum value of the function is <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>)</mo></mrow></mstyle></math> . If <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> is positive, the minimum value of the function is <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

Find the value of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> equal to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mstyle></math> .

Substitute in the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> .

Remove parentheses.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mo>⋅</mo><mn>3</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> in the expression.

Simplify each term.

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

Simplify by adding and subtracting.

Subtract <math><mstyle displaystyle="true"><mn>54</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>27</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>27</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> .

Use the <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> values to find where the minimum occurs.

Do you know how to Find the Maximum/Minimum Value f(x)=3x^2+18x+25? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | one billion seven hundred fifteen million nine hundred fifty-eight thousand seven hundred thirty |
---|

- 1715958730 has 16 divisors, whose sum is
**3096797184** - The reverse of 1715958730 is
**0378595171** - Previous prime number is
**383**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 46
- Digital Root 1

Name | two billion seventy-four million seven hundred fifty-eight thousand four hundred twenty-five |
---|

- 2074758425 has 8 divisors, whose sum is
**2159122056** - The reverse of 2074758425 is
**5248574702** - Previous prime number is
**1621**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 44
- Digital Root 8

Name | nine hundred eighty-two million twenty-one thousand five hundred thirty-six |
---|

- 982021536 has 2048 divisors, whose sum is
**18771886080** - The reverse of 982021536 is
**635120289** - Previous prime number is
**367**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 36
- Digital Root 9