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kiruha [24]
2 years ago
9

Whats the minimum and maximum value of f(x)=3(x+8)^2−10

Mathematics
1 answer:
gizmo_the_mogwai [7]2 years ago
7 0

Answer:

(-8,-10)

Step-by-step explanation:

Rewrite (x+8)2(x+8)² as (x+8)(x+8).

f(x)=3((x+8)(x+8))−10

Expand (x+8) (x+8) using the FOIL Method.

Apply the distributive property.

f(x)=3(x(x+8)+8(x+8))−10

Apply the distributive property.

f(x)=3(x⋅x+x⋅8+8(x+8))−10
Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

f(x)=3(x2+x⋅8+8x+8⋅8)−10

Move 8 to the left of x.

f(x)=3(x2+8⋅x+8x+8⋅8)−10

Multiply 8 by 8.

f(x)=3(x2+8x+8x+64)−10

Add 8x and 8x.

f(x)=3(x2+16x+64)−10

Apply the distributive property.

f(x)=3x2+3(16x)+3⋅64−10

Simplify.

Multiply 16 by 3.

f(x)=3x2+48x+3⋅64−10

Multiply 3 by 64.

f(x)=3x2+48x+192−10

Subtract 10 from 192.

f(x)=3x2+48x+182

The minimum of a quadratic function occurs at x=-\frac{b}{2a} If a is positive, the minimum value of the function is f (-\frac{b}{2a}).

Substitute in the values of aa and b.

x=−\frac{48}{2(3)}

x=-8

Replace the variable x with −8 in the expression.

f(−8)=3(−8)2+48(−8)+182

Y=-10

Therefore, the minimum value is (-8,-10) but if it is asking for just the y-value it would be -10.

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Answer:

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Step-by-step explanation:

3-1=2

2-1=1

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2 years ago
Triangle ABC has vertices at A(2,3),B(-4,-3) and C(2,-3) find the coordinates of each point of concurrency.
dem82 [27]

Answer:

Circumcenter =(-1,0)

Orthocenter =(2,-3)

Step-by-step explanation:  

Given : Points A = (2,3), B = (-4,-3), C = (2,-3)  

Formula used :  

→Mid point of two points- (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

→Slope of two points - \frac{y_2-y_1}{x_2-x_1})

→Perpendicular of a line = \frac{-1}{slope of line})

Circumcenter- The point where the perpendicular bisectors of a triangle meets.

Orthocenter-The intersecting point for all the altitudes of the triangle.

To find out the circumcenter we have to solve any two bisector equations.

We solve for line AB and AC

So, mid point of AB =(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)

Slope of AB =\frac{-3-3}{-4-2}=1

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = -1  

Equation of AB with slope -1 and the coordinates (-1,0) is,  

(y – 0) = -1(x – (-1))  

y+x=-1………………(1)  

Similarly, for AC  

Mid point of AC = (\frac{2+2}{2},\frac{3-3}{2})=(2,0)

Slope of AC = \frac{-3-3}{2-2}=\frac{-6}{0}  

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = 0  

Equation of AC with slope 0 and the coordinates (2,0) is,  

(y – 0) = 0(x – 2)  

y=0 ………………(2)  

By solving equation (1) and (2),  

put y=0 in equation (1)

y+x=-1

0+x=-1

⇒x=-1  

So the circumcenter(P)= (-1,0)

To find the orthocenter we solve the intersections of altitudes.

We solve for line AB and BC

So, mid point of AB =(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)

Slope of AB =\frac{-3-3}{-4-2}=1

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of CF = -1  

Equation of AB with slope -1 and the coordinates (-1,0) gives equation CF  

(y – 0) = -1(x – (-1))  

y+x=-1………………(3)  

Similarly, mid point of BC =(\frac{-4+2}{2},\frac{-3-3}{2})=(-1,-3)

Slope of AB =\frac{-3+3}{-4-2}=0

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of AD = 0

Equation of AB with slope 0 and the coordinates (-1,-3) gives equation AD

(y-(-3)) = 0(x – (-1))  

y+3=0

y=-3………………(4)  

Solve equation (3) and (4),

Put y=-3 in equation (3)

y+x=-1

-3+x=-1

x=2

Therefore, orthocenter(O)= (2,-3)


7 0
3 years ago
What is the arithmetic mean of the following numbers?<br> 8 10 8 5 4 7 5 10 8
Bas_tet [7]
I re-orders as 4,5,5,7,8,8,8,10,10.


Mean 7.2222222222222
Median 8
Mode 8
Range 6
Minimum 4
Maximum 10
Count n 9
Sum 65
Quartiles Quartiles:
Q1 --> 5
Q2 --> 8
Q3 --> 9
Interquartile
Range IQR 4
Outliers none
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Answer:

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3 years ago
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Answer:

The answer is B ...........

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