|
Question 1044732: when the function y= g(x)is graphed in the x-y plane, it has a minimum value at the point (1, -2). What is the maximum value of the function h(x)= -3g(x)-1?
** If possible, it would be great if there was a graph incorporated with the equation as well.
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
The given information is that g(x) has a minimum at (1,-2)
The y coordinate of that min is what we'll focus on. Multiply that by -3 to get -3*(-2) = 6. The reason why we're multiplying by -3 is because it's being multiplied by the g(x) function.
Note: multiplying all of g(x) by a negative number will flip g(x) turning the min point into a max point.
So we have -3*g(x). That's part of what makes up h(x). There's one more part: the -1 tacked on the end. So subtract 1 from that previous result of 6 to get 6-1 = 5
Therefore, the max of value of h(x) is 5
Unfortunately I cannot provide the graph because it's not clear what function g(x) is.
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
Well, there is not just one function that g(x) could be.
But it's easy to find such a function. We could use the
standard formula for a parabola,
y = a(x-h)²+k with vertex at (h,k)
to find a function with a vertex at (1,-2). To make it
easy, we choose "a" as 1, positive so it will open
upward making the vertex a minimum point.
g(x) = (x-1)²-2
Here's the graph of g(x):
Then
h(x) = -3g(x)-1
h(x) = -3[(x-1)²-2]-1
h(x) = -3(x-1)²+6-1
h(x) = -3(x-1)²+5
Compare that to y = a(x-h)+k with vertex (h,k)
and we see this parabola h(x) has vertex (1,5), which is
a maximum point because "a" is negative making the
parabola open downward: Here are both graphed together.
The red graph is g(x) and the green one is h(x).
Edwin
|
|
|
| |
