Answer:
See below.
Step-by-step explanation:
A. F(x)=3x^2 - 24x + 49
f(x) = 3(x^2 - 8x) + 49
f(x) = 3 [(x - 4)^2 - 16] + 49
f(x) = 3(x - 4)^2 - 48 + 49
f(x) = 3(x - 4)^2 + 1 <------- Vertex form. (answer).
B.
The vertex is at (4, 1). (answer).
C.
The y-intercept occurs when x = 0:
y = 3(0- 4)^2 + 1
= 3*16 + 1
= 49
The y-intercept is at (0, 49). (answer)
The x intercepts occur when y = 0:
3(x - 4)^2 + 1 = 0
3(x - 4)^2 = -1
(x - 4)^2 = -1/3
Since there is no real square root of a negative there are no x-intercepts.
(Answer)
