Negative 8 times a number minus 15 is equal to 30

Skip to content# Negative 8 times a number minus 15 is equal to 30

Mathematics ##
Comments (10) on “Negative 8 times a number minus 15 is equal to 30”

### Leave a Reply Cancel reply

Negative 8 times a number minus 15 is equal to 30

Correct option: First one -> Function 1 has the larger maximum at (4, 1).

Step-by-step explanation:

Function 1:

f(x) = -x2 + 8x - 15

To find the x-coordinate of the vertix, we can use the formula:

x_v = -b/2a

x_v = -8 / (-2) = 4

Then, to find the maximum value of f(x), we use the value of x = x_v:

f(x_v) = -4^2 + 8*4 - 15 = 1

Maximum of f(x): (4,1)

Function 2:

f(x) = -x2 + 2x - 15

To find the x-coordinate of the vertix, we can use the formula:

x_v = -b/2a

x_v = -2 / (-2) = 1

Then, to find the maximum value of f(x), we use the value of x = x_v:

f(x_v) = -1^2 + 2*1 - 15 = -14

Maximum of f(x): (1,-14)

The maximum value of function 1 is greater than the maximum of function 2 (1 is greater than -14).

Correct option: First one

[tex]y=- x^{2} +8x-15[/tex]

written in vertex form, we have,

[tex]y=-(x-4)^{2} +1[/tex],

i.e. vertex = (4, 1) and maximum value at y = 1.

[tex]y=- x^{2} +2x-3[/tex]

written in vertex form, we have,

[tex]y=-(x-1)^{2} -2[/tex],

i.e. vertex = (1, -2) and maximum value at y = -2.

Therefore, [tex]y=- x^{2} +8x-15[/tex] has the larger maximum.

Answer with explanation:

→→→Function 1

f(x)= - x²+ 8 x -15

Differentiating once , to obtain Maximum or minimum of the function

f'(x)= - 2 x + 8

Put,f'(x)=0

-2 x+ 8=0

2 x=8

Dividing both sides by , 2, we get

x=4

Double differentiating the function

f"(x)= -2, which is negative.

Showing that function attains maximum at ,x=4.

Now,f(4)=-4²+ 8× 4-15

= -16 +32 -15

= -31 +32

=1

→→→Function 2:

f(x) = −x² + 2 x − 3

Differentiating once , to obtain Maximum or minimum of the function

f'(x)= -2 x +2

Put,f'(x)=0

-2 x +2=0

2 x=2

Dividing both sides by , 2, we get

x=1

Double differentiating the function,gives

f"(x)= -2 ,which is negative.

Showing that function attains maximum at ,x=1.

f(1)= -1²+2 ×1 -3

= -1 +2 -3

= -4 +2

= -2

⇒⇒⇒Function 1 has the larger maximum.

2

Step-by-step explanation:

Step-by-step explanation:

Given are two functions and we have to find the maximum of those two

FIrst one is

[tex]f(x) = -x^2+8x-15\\f(x) = -(x^2-8x+16-16)+15\\=-(x-4)^2 +31[/tex]

Thus we changed it into vertex form

Here since leading term is negative, parabola is open down and vertex is the maximum

Maximum = (4,15)

Second one is

[tex]f(x) = -x^2+2x-15\\=-(x^2-2x+1-1)-15\\=-(x-1)^2 -14[/tex]

The above is into vertex form and also

Here since leading term is negative, parabola is open down and vertex is the maximum

Maximum = (1,-14)

Out of these two, y is greater for (4,15)

Hence I function has the larger maximum

The Function __1__ has the larger maximum.

Step-by-step explanation:

The given functions are

Function 1:

[tex]f(x)=-x^2+8x-15[/tex]

Function 2:

[tex]f(x)=-x^2+2x-15[/tex]

Both functions are downward parabola because the leading coefficient is negative. So, the vertex is the point of maxima.

If a function is [tex]f(x)=ax^2+bx+c[/tex], then its vertex is

[tex]Vertex=(\frac{-b}{2a}, f(\frac{-b}{2a}))[/tex]

The vertex of Function 1 is

[tex]Vertex=(\frac{-8}{2(-1)}, f(\frac{-8}{2(-1)}))[/tex]

[tex]Vertex=(4, f(4))[/tex]

The value of f(4) is

[tex]f(4)=-(4)^2+8(4)-15=1[/tex]

The vertex of Function 1 is (4,1). Therefore the maximum value of Function 1 is 1.

The vertex of Function 2 is

[tex]Vertex=(\frac{-2}{2(-1)}, f(\frac{-2}{2(-1)}))[/tex]

[tex]Vertex=(1, f(1))[/tex]

The value of f(1)is

[tex]f(1)=-(1)^2+2(1)-15=-14[/tex]

The vertex of Function 2 is (1,-14). Therefore the maximum value of Function 2 is -14.

Since 1>-14, therefore Function __1__ has the larger maximum.

[tex]The following graph describes function 1, and the equation below it describes function 2: function[/tex]

Function 2 has the larger maximum.

the answer is c

Step-by-step explanation:

a

Step-by-step explanation:

Function 1 written in vertex form is f(x) = -x^2 + 8x - 15 = -(x^2 - 8x + 15) = -(x^2 - 8x + 16 + 15 - 16) = -(x - 4)^2 - (-1) = -(x - 4)^2 + 1

Therefore, vertex = (4, 1)

Function 2 written in vertex form is f(x) = -x^2 + 4x + 1 = -(x^2 - 4x - 1) = -(x^2 - 4x + 4 - 1 - 4) = -(x - 2)^2 - (-5) = -(x - 2)^2 + 5

Therefore vertex = (2, 5)

Function 1 has a maximum at y = 1 and function 2 has a maximum at y = 5. Therefore, function 2 has a larger maximum.

Step-by-step explanation: