Question

Which coordinates best represents the vertex of the graph first correct answer gets Brianliest

Answer 1

`B)f(x) = {x}^(2) + 6x + 8`

Explanation:

Let
`f(x)=x^2` be the parent function. With transformation of function, firstly,we know that,

1. We can move it up or down by adding a constant to the y-value

algebraically

• g(x)=x²+C

Clearly, The parabola is moved down by 1 unit thus, C is -1. Therefore our function transforms to

• f(x)=x²-1

secondly, we know that,

• We can move it left or right by adding a constant to the x-value

algebraically,

• g(x)=(x+C)²

in case,

• C is positive, g(x) moves to the left and vise versa

Since the parabola is moved left by 3 unit, C is +3, and hence Our function eventually becomes

• 
  `f(x) = (x + 3 {)}^(2) - 1`

simplifying it yields:

`\implies \boxed{f(x) = {x}^(2) + 6x + 8}`

Hence,B is our required answer

Answer 2

The vertex of the graph is:

• the minimum point for a parabola that opens upwards
• the maximum point for a parabola that opens downwards

As this parabola opens upwards, the vertex is the minimum point.

From inspection of the graph, vertex = (-3, -1)

Equation of the graph

From inspection we can see that the x-intercepts are when
x = -4 and x = -2

`\sf x = -4 \implies x+4=0`

`\sf x = -2 \implies x+2=0`

Therefore:

`\sf y=(x+4)(x+2)`

Expand:

`\sf \implies y=x^2+6x+8`