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ozzi
3 years ago
14

A rectangular whiteboard has an area of x^2-12x-45. Which expression could

Mathematics
1 answer:
Firdavs [7]3 years ago
4 0

Answer: I Think it is b

Step-by-step explanation:

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Which function has a vertex on the y-axis? f(x) = (x – 2)2 f(x) = x(x + 2) f(x) = (x – 2)(x + 2) f(x) = (x + 1)(x – 2)
strojnjashka [21]

we know that

If the vertex is on the y-axis, then the x-coordinate of the vertex is equal to zero

we are going to verify the vertex of each one of the functions to determine the solution

Remember that

The equation in vertex form of a vertical parabola is equal to

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

where

(h,k) is the vertex

if a>0 -------> the parabola open upward (vertex is a minimum)

if a -------> the parabola open downward (vertex is a maximun)

<u>case A)</u> f(x)=(x-2)^{2}

This is a vertical parabola open upward

the vertex is the point (2,0)

therefore

The function f(x)=(x-2)^{2}  does not have a vertex on the y-axis

<u>case B)</u> f(x)=x(x+2)

f(x)=x(x+2)=x^{2}+2x

convert to vertex form

Complete the square. Remember to balance the equation by adding the same constants to each side.

f(x)+1=x^{2}+2x+1

Rewrite as perfect squares

f(x)+1=(x+1)^{2}

f(x)=(x+1)^{2}-1

the vertex is the point (-1,-1)

therefore

The function f(x)=x(x+2) does not have a vertex on the y-axis

<u>case C)</u> f(x)=(x-2)(x+2)

f(x)=(x-2)(x+2)=x^{2}-2^{2}

f(x)=x^{2}-4

the vertex is the point (0,-4)

The x-coordinate of the vertex is equal to zero

therefore

The function f(x)=(x-2)(x+2) has a vertex on the y-axis

<u>case D)</u> f(x)=(x+1)(x-2)

f(x)=(x+1)(x-2)\\ \\f(x)= x^{2}-2x+x-2 \\ \\f(x)= x^{2} -x-2

convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)+2= x^{2} -x

Complete the square. Remember to balance the equation by adding the same constants to each side.

f(x)+2+0.25= x^{2} -x+0.25

f(x)+2.25= x^{2} -x+0.25

Rewrite as perfect squares

f(x)+2.25= (x-0.50)^{2}

f(x)=(x-0.50)^{2}-2.25

the vertex is the point (0.5,-2.25)

therefore

The function f(x)=(x+1)(x-2) does not have a vertex on the y-axis

<u>the answer is</u>

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

6 0
3 years ago
Read 2 more answers
Select the two figures that are similar to each other.
kakasveta [241]

Answer:

B and D

Step-by-step explanation:

if they had letters it would be

A     B

C     D

options B and D are similar

7 0
3 years ago
Read 2 more answers
I need help bro!!!!!!!
konstantin123 [22]

Answer:

The one that is on the bottom half and on the right side.

Step-by-step explanation:

(0,30) to (10,0)

Because the x value 0 represents the time in which the paint job started and ends in the value 10

While the y value 30 is the amount of paint he started with and ends with 0

5 0
3 years ago
Diego has purchased a $159,000 home with a 30-year mortgage at 5.05%. He can make a monthly payment of $1,300. If he were to mak
Gemiola [76]

Answer: 173 months MY GUY!

Step-by-step explanation:

3 0
3 years ago
712.9 Divided by what equals 71.29
soldi70 [24.7K]

Answer:

10

Step-by-step explanation:

712.9 / 10 = 71.29

3 0
3 years ago
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