Which of the following could be its equation?

So to solve problems like these you can work out each equation by substituting the x and y with the coords from the vertex (2,-4) and which ever one is true is the corresponding equation.

Lets try the first one

A) y = 2( x-2)^2-4    this would become

  -4 = 2(2-2)^2-4    we solve this and get

   -4 = 2(0)-4

   -4 = -4  

so it seems like A is the correct answer, of course we'd wanna check out the other answers just to be sure.

Lets try one and do C

C)  -2 = 2(-4-2)^2+2  

    -2 = 2(-8)^2+2

    -2 = 130

These aren't equal so this can't be our equation

So you can also do one more just to be super sure you have the right answer but I think A is the correct one :)

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step-by-step explanation:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is