Question

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

Answer 1

Answer:

Graph A.

Step-by-step 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

$y=(\frac{x+9}{2})^{2}-\frac{81}{4}+14$

  $=(x+4.5)^{2}-6.25$

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.

Answer 2

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.