QuestionFind the minimum value of the function $f(x) = x^{2} - 6x + 14$ . Options: A) -3, B) 3, C) 5, D) 14.

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=x^{}-6 x+14$ . We need to find the minimum value of the function $f(x)$

STEP 2

The function $f(x)=x^{2}-6 x+14$ is a quadratic function. The general form of a quadratic function is $f(x)=ax^{2}+bx+c$ , where $a$ , $b$ , and $c$ are constants.The minimum or maximum value of a quadratic function occurs at $x=-\frac{b}{2a}$ .

STEP 3

In our function $f(x)=x^{2}-6 x+14$ , we can identify $a=1$ , $b=-6$ , and $c=14$ .

STEP 4

Substitute $a=1$ and $b=-6$ into the formula $x=-\frac{b}{2a}$ to find the $x$ value at which the minimum occurs.
$x=-\frac{-6}{2(1)}$

STEP 5

Calculate the $x$ value.
$x=-\frac{-}{2(1)} =3$

STEP 6

Now that we have the $x$ value, we can substitute this into the function $f(x)$ to find the minimum value.
$f(3)=3^{2}-6(3)+14$

STEP 7

Calculate the value of $f(3)$ .
$f(3)=3^{2}-6(3)+14 =9 -18 +14 =5$ The minimum value of the function $f(x)=x^{2}-6 x+14$ is5.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms