Answer:
The range of the equation is y ≥ 9 ⇒ C
Step-by-step explanation:
The quadratic equation y = ax² + bx + c, represents by a parabola of vertex (h, k), where h = [tex]\frac{-b}{2a}[/tex] and k is the value of y at x = h
- The range of the quadratic if it has a minimum vertex is y ≥ k, and y ≤ k if it has a maximum vertex
- The parabola has a minimum vertex if the value of a is positive and a maximum vertex if the value of a is negative
∵ The equation is y = x² + 9
→ Compare it with the form above to find a and b
∴ a = 1 and b = 0
∵ a is a positive number
∴ The parabola has a minimum vertex
→ By using the 1st rule above
∴ The range is y ≥ k
→ Use the rule of h above to find it
∵ h = [tex]\frac{-(0)}{2(1)}[/tex] = [tex]\frac{0}{2}[/tex]
∴ h = 0
→ To find k substitute x by the value of h and y by k
∵ k = (0)² + 9
∴ k = 0 + 9
∴ k = 9
∴ The range of the equation is y ≥ 9
