Question

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

Answer 1

Answer:

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:

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

Answer 2

Answer:

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

Step-by-step 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