SOLUTION: Tell whether the function has a minimum value or a maximum value for the following two problems separately. Then find the value. f(x) = -4x^2 - 24x + 15 f(x) = 6x^2 + 36x - 2

Algebra ->  Functions -> SOLUTION: Tell whether the function has a minimum value or a maximum value for the following two problems separately. Then find the value. f(x) = -4x^2 - 24x + 15 f(x) = 6x^2 + 36x - 2      Log On


   

Question 1091440: Tell whether the function has a minimum value or a maximum value for the following two problems separately. Then find the value.
f(x) = -4x^2 - 24x + 15

f(x) = 6x^2 + 36x - 20
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+-4x%5E2+-+24x+%2B+15+
The function has a maximum since the first term -4x%5E2 has a negative coefficient.
To find the max, you need to find the axis of symmetry first, and to find the axis of symmetry, use this formula:
x=-b%2F%282a%29

From the equation f%28x%29+=+-4x%5E2+-+24x+%2B+15 we can see that a=-4 and b=-24
x=-%28-24%29%2F%282%2A-4%29
x=24%2F%28-8%29
x=+-3
So the axis of symmetry is x=-3, and it is the x-coordinate of the vertex is x=-3.
Lets plug this into the equation to find the y-coordinate of the vertex.
Lets evaluate f%28-3%29
f%28-3%29=-4%2A%28-3%29%5E2+-+24%2A%28-3%29+%2B+15
f%283%29=-36+%2B72+%2B+15
f%283%29=51
So the vertex is (-3,51)
So that means the functions highest value is 51 which means the functions maximum is:51



2.
f%28x%29+=+6x%5E2+%2B+36x+-+20
The function has a minimum since the first term 6x%5E2 has a positive coefficient.
To find the min, you need to find the axis of symmetry first:
x=-b%2F%282a%29
x=-36%2F%282%2A6%29
x=-36%2F12
x=-3
So the axis of symmetry is x=-3, and it is the x-coordinate of the vertex is x=-3.
Lets plug this into the equation to find the y-coordinate of the vertex.
Lets evaluate f%28-3%29%7D%7D%0D%0A%0D%0A%7B%7B%7Bf%28x%29+=+6%28-3%29%5E2+%2B+36%28-3%29+-+20
f%28x%29+=+54+-108+-+20
f%28x%29+=++-74
So the vertex is (-3,-74)
So that means the functions highest value is -74 which means the functions maximum is:-74