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3 years ago

The vertex of this parabola is at (-3, 2). Which of the equations below could be its equation?

Mathematics

1 answer:

kap26 [50]3 years ago

8 0

The correct answer is d hope i helped

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WARRIOR [948]

Answer:

$2\,(x-1)^2=4$

which is the first option in the list of possible answers.

Step-by-step explanation:

Recall that the minimum of a parabola generated by a quadratic expression is at the vertex of the parabola, and the formula for the vertex of a quadratic of the general form:

$y=ax^2+bx+c$

is at $x_{vertex}=\frac{-b}{2\,a}$

For our case, where $a=2\,\,, b=-4\,\,,\,\,and \,\,c=-2$ we have:

$x_{vertex}=\frac{-b}{2\,a}\\x_{vertex}=\frac{4}{2\,*\,2}\\x_{vertex}=1$

And when x = 1, the value of "y" is:

$y(x)=2x^2-4x-2\\y(1)=2(1)^2-4(1)-2\\y(1)=2-6\\y(1)=-4\\y_{vertex}=-4$

Recall now that we can write the quadratic in what is called: "vertex form" using the coordinates $(x_{vertex},y_{vertex)$ of the vertex as follows:

$y-y_{vertex}=a\,(x-x_{vertex})^2$

Then, for our case:

$y-(-4)=2\,(x-1)^2\\y=2\,(x-1)^2-4$

Then, for the quadratic equal to zero as requested in the problem, we have:

$y=2\,(x-1)^2-4=0\\2\,(x-1)^2-4=0\\2\,(x-1)^2=4$

5 0

3 years ago

X an y are proportional. What is the missing value in the table <br>

Leto [7]

Answer:

X+y

Step-by-step explanation:

6 0

3 years ago

If x equals 12 and y equals 9 find the value of 2 x - 2y

Genrish500 [490]

2 ( 12) - 2 (9)

24 - 18

6 answer

4 0

4 years ago

Y=8-2x when x=8 the value of y

Lera25 [3.4K]

Answer:

-8

Step-by-step explanation:

Given that x and y are two variables. they are related by the function

y =8-2x

Since x and y are related, given one value we can find the other using this equation.

In our question, given that x =8

Substitute x value in the equation

y = 8-2x

y =8-2(8) = -8

Hence answer is -8:

Verify: We verify by putting -8 for y and check whether x =8

-8=8-2x

Or 2x = 16

x =8

Verified

8 0

3 years ago

Read 2 more answers

What happens to the function f(x)=(x−1)2+1 when it becomes f′(x)=2((x−1)2+1)?

Ymorist [56]

Answer: c

Step-by-step explanation: I took the test

7 0

3 years ago

Read 2 more answers