##### (c) Find its maximum or minimum value. f(x) =

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

f(x) = 8x2 − 16x + 1
(a) Express the quadratic function in standard form.
 f(x) =

(c) Find its maximum or minimum value.

f(x) =

Jul 6th, 2015

The given equation is 8 x^2-16x+1

Here a= 8, b= -16 and c= 1

Using the formula

x= -{b+-(b^2-4ac)}/2a Put the values of a,b and c.

We get x1= 1+1/4 sqrt 14

x2= 1-1/4 sqrt 14

To find the maximum and minimum value, we will use Perfect square method.

Make the coefficient of  positive by multiplying it by  in case.
Maxima / Minima is decided from the sign of 'a'.
If 'a' is positive then we have Minima and for 'a'negative we have Maxima.

Step two:
Now make the perfect square with the same  and  coefficient.

Maxima / Minima lies at the point where this squared term is equal to zero.

Hence,
=>

This point is a minima if value of coefficient of x2 is positive and vice versa. For our function the point x=1 is a .

Jul 6th, 2015

...
Jul 6th, 2015
...
Jul 6th, 2015
Oct 18th, 2017
check_circle
The text passage contains a mathematical question related to a quadratic function, and it provides a detailed solution for finding the maximum or minimum value of the function.
single_question_with_answer
- the question is to find the maximum or minimum value of the quadratic function \( f(x) = 8x^2 - 16x + 1 \).
- the answer is provided, showing the steps to find the minimum value of the function, which occurs at \( x = 1 \).
- the minimum value of the function is \( f(1) = -7 \).
- the solution also includes the steps to find the roots of the quadratic equation using the quadratic formula.
- the roots are \( x_1 = 1 + \frac{\sqrt{14}}{4} \) and \( x_2 = 1 - \frac{\sqrt{14}}{4} \).

however, the minimum value \( f(1) = -7 \) is not explicitly stated in the provided solution, but it can be derived from the steps given.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
##### (c) Find its maximum or minimum value. f(x) =

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

f(x) = 8x2 − 16x + 1
(a) Express the quadratic function in standard form.
 f(x) =

(c) Find its maximum or minimum value.

f(x) =

Jul 6th, 2015

The given equation is 8 x^2-16x+1

Here a= 8, b= -16 and c= 1

Using the formula

x= -{b+-(b^2-4ac)}/2a Put the values of a,b and c.

We get x1= 1+1/4 sqrt 14

x2= 1-1/4 sqrt 14

To find the maximum and minimum value, we will use Perfect square method.

Make the coefficient of  positive by multiplying it by  in case.
Maxima / Minima is decided from the sign of 'a'.
If 'a' is positive then we have Minima and for 'a'negative we have Maxima.

Step two:
Now make the perfect square with the same  and  coefficient.

Maxima / Minima lies at the point where this squared term is equal to zero.

Hence,
=>

This point is a minima if value of coefficient of x2 is positive and vice versa. For our function the point x=1 is a .

Jul 6th, 2015

...
Jul 6th, 2015
...
Jul 6th, 2015
Oct 18th, 2017
check_circle
user
The text passage contains a mathematical question related to a quadratic function, and it provides a detailed solution for finding the maximum or minimum value of the function.

TYPE: SINGLE_QUESTION_WITH_ANSWER
- The question is to find the maximum or minimum value of the quadratic function \( f(x) = 8x^2 - 16x + 1 \).
- The answer is provided, showing the steps to find the minimum value of the function, which occurs at \( x = 1 \).
- The minimum value of the function is \( f(1) = -7 \).
- The solution also includes the steps to find the roots of the quadratic equation using the quadratic formula.
- The roots are \( x_1 = 1 + \frac{\sqrt{14}}{4} \) and \( x_2 = 1 - \frac{\sqrt{14}}{4} \).

However, the minimum value \( f(1) = -7 \) is not explicitly stated in the provided solution, but it can be derived from the steps given.