All categories

3 years ago

Which of the following is the minimum value of the equation y = 3x^2 − 4x − 2?

Mathematics

1 answer:

KonstantinChe [14]3 years ago

5 0

Answer:

-3 1/3

Step-by-step explanation:

The quadratic

... y = ax² +bx +c

has its extreme value at

... x = -b/(2a)

Since a = 3 is positive, we know the parabola opens upward and the extreme value is a minimum. (We also know that from the problem statement asking us to find the minimum value.) The value of x at the minimum is -(-4)/(2·3) = 2/3.

To find the minimum value, we need to evaluate the function for x=2/3.

The most straightforward way to do this is to substitue 2/3 for x.

... y = 3(2/3)² -4(2/3) -2 = 3(4/9) -8/3 -2

... y = (4 -8 -6)/3 = -10/3

... y = -3 1/3

_____

Confirmation

You can also use a graphing calculator to show you the minimum.

You might be interested in

Which of the following are examples of a geometric sequence? Select any and all that apply: may be more than one correct answer.

nevsk [136]

Answer:

( 1 , -2 , 4 , -8 , 16 , ... )

( 9 , 3 , 1 , 1/3 , 1/9 , ... )

Step-by-step explanation:

A geometric sequence has a common ratio in consecutive terms,

In sequence,

$1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....$

$\frac{1/2}{1}\neq \frac{1/6}{1/2}\neq \frac{1/24}{1/6}\neq \frac{1/120}{1/24}...$

i.e.

$1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....$ is not a Geometric sequence,

1 , -2 , 3 , -4 , 5 , ...

$\frac{-2}{1}\neq \frac{3}{-2}\neq \frac{-4}{3}\neq \frac{5}{-4}...$

i.e. 1 , -2 , 3 , -4 , 5 , ... is not a Geometric sequence,

In sequence,

1 , -2 , 4 , -8 , 16 , ...

$\frac{-2}{1}=\frac{4}{-2}= \frac{-8}{4}= \frac{16}{-8}...$

i.e. 1 , -2 , 4 , -8 , 16 , .... is a Geometric sequence,

In sequence,

0 , 1 , 0 , -1 , 0 , .....

$\frac{1}{0}\neq \frac{0}{1}\neq \frac{-1}{0}\neq \frac{0}{-1}...$

i.e. 0 , 1 , 0 , -1 , 0 , .....is not a Geometric sequence,

In sequence,

9 , 3 , 1 , 1/3 , 1/9 , ...

$\frac{3}{9}=\frac{1}{3}= \frac{1/3}{1}= \frac{1/9}{1/3}...$

i.e. 9 , 3 , 1 , 1/3 , 1/9 , ... is a Geometric sequence,

In sequence,

1 , 3 , 5 , 7 , 9 , ...

$\frac{3}{1}\neq \frac{5}{3}\neq \frac{7}{5}\neq \frac{9}{7}...$

i.e. 1 , 3 , 5 , 7 , 9 , ... is not a Geometric sequence

4 0

3 years ago

What is the value of x? HELP! Please

Anastaziya [24]

D. 68
I don’t remember what formula this is called but the formula says that all angles in a triangle should add up to 180, so 75+37= 112, 180-112= 68

8 0

3 years ago

Read 2 more answers

Which expression gives the distance between the points

Anna35 [415]

Answer:

D. √((2 +4)² +(5 -8)²)

Step-by-step explanation:

The distance is found using the formula ...

d = √((x1 -x2)² +(y1 -y2)²)

Selection D has this formula properly filled in with the values ...

(x1, y1) = (2, 5)

(x2, y2) = (-4, 8)

6 0

3 years ago

How I divided a hexagon into 3 equal parts ?

Furkat [3]

It splits into 6 easerly so just make each part double walls as the pic shows

3 0

3 years ago

On a coordinate grid, Ming's house is located 2 blocks to the right and blocks up from (0. 0). Joe's house is located 3 blocks t

kolbaska11 [484]

If on a coordinate grid, Ming's house is located 2 blocks to the right and (I suppose also 2) blocks up from (0. 0), then the ordered pair that describes the location of Ming's house is (2,2) (moving right 2 units from some point you have to add 2 units to the x-coordinate of the point from which you are moving and moving up 2 units from this point you have to add 2 units to y-coordinate of the point from which you are moving up).

If Joe's house is located 3 blocks to the right and 2 blocks down from Ming's house, then the ordered pair that describes the location of Ming's house is (2+3,2-2), that is (5,0) (moving right 3 units from some point you have to add 3 units to the x-coordinate of the point from which you are moving and moving down 2 units from the point you have to substract 2 units from y-coordinate of the point from which you are moving down).

3 0

3 years ago