Question

Which of the following functions best describes this graph?

Answer 1

Heyyyy!!!!! I'm going to say choice A

Answer 2

Answer:

A. $y=x^2+9x+18$

Step-by-step explanation:

By the given graph,

The function is intersecting x-axis at - 3 and - 6,

Thus, the x-intercepts of the given function must be (-3,0) and (-6,0),

Now, In option  A,

The function is,

$y=x^2+9x+18$

For x-intercept y = 0,

$x^2+9x+18=0$

$x^2+6x+3x+18=0$

$x(x+6)+3(x+6)=0$

$(x+3)(x+6)=0$

$\implies x = -3\text{ or }x = -6$

⇒ x-intercepts are (-3,0), (-6,0)

⇒ The function $y=x^2+9x+18$ describes the given graph,

Now, In option  B,

The function is,

$y=(x-3)(x-6)$

For x-intercept y = 0,

$(x-3)(x-6)=0$

$\implies x = 3\text{ or }x = 6$

⇒ x-intercepts are (3,0), (6,0)

⇒ The function $y=(x-3)(x-6)$ does not describe the given graph,

Now, In option  C,

The function is,

$y=x^2-2x+4$

For x-intercept y = 0,

$y=x^2-2x+4=0$

$(x-2)^2=0$

$\implies x = 2$

⇒ x-intercept is (2,0),

⇒ The function $y=x^2-2x+4$ doesn't describe the given graph,

Now, In option D,

The function is,

$y=(x+5)(x-4)$

For x-intercept y = 0,

$(x+5)(x-4)=0$

$\implies x = -5\text{ or }x = 4$

⇒ x-intercepts are (-5,0), (4,0)

⇒ The function $y=(x+5)(x-4)$ does not describe the given graph.