Question

Which graph is defined by the function given below? y=(x+2)(x+7)

Answer 1

Answer: Graph A
We can determine the x-intercepts from the equation. X-intercepts are x=-2 and x=-7 which is what Graph A shows.

Answer 2

Graph A.

Explanation:

The given graph in the question is y = (x + 2) (x + 7)

or y = x² + 2x + 7x + 14

= x² + 9x + 14

Now we convert this equation of parabola in vertex form

`y=((x+9)/(2))^(2)-(81)/(4)+14`

`=(x+4.5)^(2)-6.25`

This equation is in the form of y = (x-h)² + k where (h,k) is the vertex.

So in the given equation y = (x + 4.5)² - 6.25

Vertex should be (-4.5, 6.25) which lies in third quadrant.

Therefore, option A. is the graph.