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)
To determine an equation for the function with the given 3 pieces, you can use the concept of piecewise functions. A piecewise function is a function that is defined by different algebraic expressions on different intervals of its domain.
To create the equation for the function, you need to define the expression for different intervals based on the given equations.
First, let's consider the interval where f1(x) is defined. The equation f1(x) = 0 implies that this piece is simply a horizontal line passing through the x-axis at y = 0.
Next, let's consider the interval where f2(x) is defined. The equation f2(x) = 1/8(x+16)^2 - 98 represents a quadratic function in vertex form. The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
In this case, we have f2(x) = 1/8(x + 16)^2 - 98, where (h, k) = (-16, -98). So, the vertex of the parabola is (-16, -98).
Lastly, let's consider the interval where f3(x) is defined. The equation f3(x) = 2x + 24 represents a linear function.
To combine all three pieces into one equation, we can use the concept of piecewise functions. The equation for the function can be written as:
f(x) = { 0, x ≤ a,
1/8(x + 16)^2 - 98, a ≤ x ≤ b,
2x + 24, x ≥ b }
where the values of 'a' and 'b' depend on the specific range of the function.
Please note that without the specified range of the function, it is not possible to determine the exact values of 'a' and 'b'.