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Charra [1.4K]
3 years ago
14

The functions f(x) = -(x+4) +2 and g(x) =(x-2)^2 -2 have been rewritten using the completing the square method. Apply your knowl

edge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning
Mathematics
1 answer:
rewona [7]3 years ago
4 0

Answer:

g(x) = (x-2)^2 -2

If we compare this function with the vertex form we see that:

a = 1, h =2, k =-2

So then the vertex would be (h,k)=(2,-2)

And since the value for a is positive we know that the parabola open upward. We don't have a maximum defined since open upwards and the minimum point correspond to the vertex on this case (2,-2).

f(x)= -(x+4)^2 +2

If we compare this function with the vertex form we see that:

a=-1, h =-4, k = 2

And since the value for a is negative we know that the parabola open downward. We don't have a minimum defined since open downwards and the maximum point correspond to the vertex on this case (-4,2).

Step-by-step explanation:

We need to remember that the standard form for a parabola is given by the following equation:

y = ax^2 + bx +c

And the vertex form is given by this formula:

y = a(x-h)^2 +k

And we want to find the vertex and if we have a maximum or minimum for each function. Let's begin with g(x)

g(x) = (x-2)^2 -2

If we compare this function with the vertex form we see that:

a = 1, h =2, k =-2

So then the vertex would be (h,k)=(2,-2)

And since the value for a is positive we know that the parabola open upward. We don't have a maximum defined since open upwards and the minimum point correspond to the vertex on this case (2,-2).

For the function f(x) we assume that we have the following equation:

f(x)= -(x+4)^2 +2

If we compare this function with the vertex form we see that:

a=-1, h =-4, k = 2

And since the value for a is negative we know that the parabola open downward. We don't have a minimum defined since open downwards and the maximum point correspond to the vertex on this case (-4,2).

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Allisa [31]

Answer:

56/7 is 8 so 8x4 is 32 is is easy

4 0
2 years ago
Given the following system of equations: -4x+8=16, 2x+4y=32 what action was completed to create this new equivalent system of eq
castortr0y [4]

The equation (1) is divided by 2 to create new equivalent system of equations.

Step-by-step explanation:

The given systems of equations are:

-4x+8y=16\,\,\,(1)\\2x+4y=32\,\,\,(2)

Considering 8y instead of 8 in eq(1)

We need to identify  what action was completed to create this new equivalent system of equations? -2x+4y=8, 2x+4y=32

Comparing given equations we came to know that equation(1) is divided by 2 to get the new equation i.e

-4x+8y=16\\Divide\,\,by\,\,2:\\-2x+4y=8

While second equation is same as given.

So, The equation (1) is divided by 2 to create new equivalent system of equations.

Keywords:System of Equation

Learn more about System of Equation at:

  • brainly.com/question/9045597
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#learnwithBrainly

4 0
2 years ago
(1 - 5q ) +2 (2.5q +8 )
VikaD [51]
Distribute
remember
a(b+c)=ab+ac
2(2.5q+8)=2(2.5q)+2(8)=5q+16

1-5q+5q+16
1+0+16
17
5 0
3 years ago
Which of the following represents x =1/3y written in general form?
Serhud [2]

If you would like to write x = 1/3 * y in general form, you can do this using the following steps:

The general form of the equation is: ax + by + c = 0.

x = 1/3 * y

x - 1/3 * y = 0


The correct result would be x - 1/3 * y = 0.

4 0
3 years ago
Function 1 is defined by the equation p=r + 7.
MariettaO [177]

Answer:

Function 2

Step-by-step explanation:

Function 1 has a slope of 1.

Function 2 has a slope of 1.1.

1.1 > 1, so Function 2 has a greater slope.

4 0
3 years ago
Read 2 more answers
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