Please I need help with this algebra problem
With the 3 equations
f1(x)=0
f2(x)=1/8(x+16)^2-98
f3(x)=2x+24
Determine an equation for this function with the 3 pieces above.(Refer to creating the polynomial functions)
no idea what you want to do.
We could make
g(x) = f2(x) - f3(x)
or whatever you want to do. What do you mean when you say "this function"?
thats where I'm stuck at
i have even seen an example like this in the lesson
how would i minus the f(2)x by f(3)x
oh please - just use their definition!
f2(x) - f3(x) = (1/8 (x+16)^2-98) - (2x+24)
You might want to simplify that to
x^2/8 +2x -90
To determine an equation for the function, we need to combine the three given equations into a single equation.
The given equations are:
f1(x) = 0
f2(x) = 1/8(x+16)^2 - 98
f3(x) = 2x + 24
Since f1(x) is always zero, it does not contribute to the overall function. Therefore, we only need to consider f2(x) and f3(x) in creating the equation.
To combine the two equations, we need to consider the domain over which each equation is valid. For f2(x), the equation is valid for all real numbers, x. However, for f3(x), it does not have any restrictions on the domain since it is defined for all real numbers as well. Therefore, we can use the entire domain for the combination of the equations.
The equation for the function with the three given pieces can be written as follows:
f(x) = 1/8(x+16)^2 - 98 for x ≤ k
f(x) = 2x + 24 for x > k
Here, k represents the value of x where the two equations transition from one to the other. To find the value of k, we need to set f2(x) equal to f3(x) and solve for x:
1/8(x+16)^2 - 98 = 2x + 24
Simplifying this equation will give us the value of k, which we can then substitute into the final equation.
I hope this explanation helps you understand how to determine the equation for a function given multiple pieces. If you need further assistance, please feel free to ask.