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statuscvo [17]
3 years ago
12

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)

Mathematics
2 answers:
Zina [86]3 years ago
8 0
The answer is F(X)=(x-2)(x+2)
strojnjashka [21]3 years ago
6 0

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)

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algol13

Answer:

6/5 or 1 1/5

Step-by-step explanation:

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~Multiply both numerators and denominators together

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Best of Luck!

7 0
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Translate the sentence into an inequality. Twice the difference of a number and 8 is at least 26 . Use the variable w for the un
Olin [163]
"At least" refers to greater than or equal to (≥).
This is because "at least" means:
- it can't be less than
- it can be equal to
- it can be greater than
This is basically like saying no less than.
If you must have at least 10 oranges for some recipe, then you must have 10 oranges, but you can also have more.

"Twice the difference of a number and 8"
This means that 2 times a number minus 8.
This can be written as 2(w - 8), since w is unknown and it's the difference between w and 8.
The 2 is being multiplied by this because it's 2 times this difference.

"At least 26"
This means ≥ 26.

Now for the actual inequality.
"Twice the difference of a number and 8"
translates to 2(w - 8)
"is at least 26"
translates to ≥ 26
Now put them together.
2(w - 8) ≥ 26

So the answer is 2(w - 8) ≥ 26.

Hope this helps! :)
7 0
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patriot [66]
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3 0
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klemol [59]

Answer:

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Step-by-step explanation:

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9

4 0
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