Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. y=x^2+x+9 a. D: all real numbers R: (y ≤ 8.75) b. D: (x ≥ 0) R: (y ≥ 0) c. D: all real numbers R: (y ≥ 8.75) d. D: all real numbers R: (y ≥ - 8.75)

Answer: Option c. D: all real numbers R: (y ≥ 8.75)

Solution:

y=x^2+x+9

Domain: all real numbers = ( - Infinite, Infinite)

y=ax^2+bx+c

a=1 > 0, the parabola opens upward: Range: y ≥k

b=1

c=9

Vertex: V = (h, k)

h=-b / (2a)

h=-1 / (2 (1))

h=-1/2

h=-0.5

k=y=h^2+h+9

k = (-0.5) ^2 + (-0.5) + 9

k=0.25-0.5+9

k=8.75

Range: y≥k

Range: y≥8.75