Answer:
The minimum value is 2.8. The vertex is (-7, 2.8).
Explanation:
Through the x^2 term we identify this as a quadratic function whose graph opens up. The minimum value of this function occurs at the vertex (h, k). The x-coordinate of the vertex is
-b 11.2
x = --------- which here is x = - ------------ = -7
2a 2(0.8)
We need to calculate the y value of this function at x = -7. This y-value will be the desired minimum value of the function.
Substituting -7 for x in the function f(x) = 0.8x^2 + 11.2x + 42 yields
f(-7) = 0.8(-7)^2 + 11.2(-7) + 42 = 2.8
The minimum value is 2.8. The vertex is (-7, 2.8).