Asked by joe
determine the given quadratic function has a minimum valueor maximum vale. Then find the coordinates of the minimum or maximum point.
f(x)=x^2=2x-9
f(x)=x^2=2x-9
Answers
Answered by
Reiny
Your parabola opens up because of +x^2, so it has a minimum
to find min, 3 methods:
1. by Calculus,
f ' (x) = 2x + 2
= 0 for a min of f(x)
2x = -2
x=-1
f(-1) = 1 - 2 - 9 = -10
2. complete the square to find the vertex:
f(x) = x^2 + 2x + 1 -1 -9
=(X+1)^2 - 10
the vertex is (-1,-10)
so there is a min of -10 when x = -1
3. by formula
if f(x)= ax^2 + bx + c, the x of the vertex is -b/2a
x of vertex = -2/(2(1)) = -1
f(-1) = -10 , as above
to find min, 3 methods:
1. by Calculus,
f ' (x) = 2x + 2
= 0 for a min of f(x)
2x = -2
x=-1
f(-1) = 1 - 2 - 9 = -10
2. complete the square to find the vertex:
f(x) = x^2 + 2x + 1 -1 -9
=(X+1)^2 - 10
the vertex is (-1,-10)
so there is a min of -10 when x = -1
3. by formula
if f(x)= ax^2 + bx + c, the x of the vertex is -b/2a
x of vertex = -2/(2(1)) = -1
f(-1) = -10 , as above
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.