Question #abef5

1 Answer
May 9, 2017

Answer:

Min: #(-3.5, -3.25)#
Roots: #x~=-5.3028# and #x~=-1.6972#

Explanation:

This polynomial is in the form

#y=ax^2+bx+c#

Where
#a=1#
#b=7#
#c=9#

The #x#-value of the minimum point of the parabola is given by

#x_min=-b/(2a)=-7/2~=-3.5#

The minimum #y#-value occurs when you plug that #x_min# into #y#

#y_min=(-7/2)^2+7(-7/2)+9=-13/4~=-3.25#

So the minimum point of the parabola is at the point #(-3.5, -3.25)#

Finally, you find where the parabola crosses the #x#-axis by plugging the given equation into the quadratic formula using #a#, #b#, and #c# from above.

#x=(-b+-sqrt(b^2-4ac))/(2a)#
#x=(-7+-sqrt((-7)^2-4(1)(9)))/(2(1))#
#x=-7+-1/2sqrt(13)#
So, #x~=-5.3028# and #x~=-1.6972#

Graphing gives:
graph{x^2+7x+9 [-6.4, 0.1, -3.49, 0.408]}