A function has a minimum value of 24 and x-intercepts of -8 and 2. What is the value of x that minimizes the function?

Question

it's multiple choice and the options are:

a. 12

b. -3

c. -2

d. 2

Answer 1

minimum f(x) = 24, the point (x,24)

x intercepts: -8 and 2

(-8,0) and (2,0)

but if 24 is the minimum value of f(x), then the graph doesn't intersect the y axis and there would be no x intercepts

maybe the problem was that 24 is the maximum value, then

axis of symmetry is the average of the intercepts -8 and 2 (-8+2)/2 = -3

b) is then the correct answer

y = -(x+3)^2 + 24 where (-3,24) is the vertex and maximum point of a downward opening parabola

y=-(x-h)^2 +k is in vertex form where (h,k) = vertex = (-3,24)