Answer:
The function in the vertex form is y = (x + 2.5)² - 15.25
Step-by-step explanation:
The vertex form of the quadratic function y = ax² + bx + c is:
y = a(x - h)² + k, where
∵ The given function is y = x² + 5x - 9
∴ a = 1, b = 5, c = -9
→ Use a and b to find h
∵ h = [tex]\frac{-b}{2a}[/tex]
∴ h = [tex]\frac{-5}{2(1)}=-2.5[/tex]
∴ h = -2.5
→ Find y at x = -2.5
∵ y = (-2.5)² + 5(-2.5) - 9 = 6.25 - 12.5 - 9
∴ y = -15.25
∴ k = -15.25
→ Substitute a, h, k in the vertex form above
∴ y = 1(x - -2.5)² + -15.25
∴ y = (x + 2.5)² - 15.25
The function in the vertex form is y = (x + 2.5)² - 15.25
