Question

The graph Of y= x2 + 11x + 24 is equivalent to the graph of which equation?

Answer 1

Answer:

Step-by-step explanation:

Please use " ^ " to indicate exponentation:   y= x^2 + 11x + 24.  Thanks.

Because x^2 is positive, the graph of this parabola opens up.

We can find the vertex and roots (zeros) as follows, using the quadratic formula:

With a = 1, b = 11 and c = 24,

       -11  ± √ [ (11^2-4(1)(24) ]       -11 ± √25

x = ------------------------------------ = --------------- = -3    and   x = -8

              2(1)                                     2

This tells us that the x-intercepts are at (-3, 0) and (-8, 0).  The minimum value is at x = -b / (2a), which here is x = -11 / [2] = -5 1/2 (which is halfway between the zeros).

The vertex (and thus, the minimum) is at (-5 1/2, f(-5 1/2) ).