Final answer:
The function y=-16x²+9x+4 is nonlinear because it contains the term -16x², which involves x raised to the second power. Linear functions only have variables raised to the power of 1.
Step-by-step explanation:
- The function in question is y=-16x²+9x+4. To determine whether it is linear or nonlinear, we need to look at the highest power of the variable x.
- If the highest power of x is 1, then the function is linear, which means it will graph as a straight line.
- However, if there is a variable raised to a power higher than 1, then the function is nonlinear and will not graph as a straight line.
- In this case, we have the term -16x² which indicates that x is raised to the second power.
- Because this is higher than 1, the function is non-linear.
- An example of a linear equation would be in the form of y = a + bx, where a is the y-intercept, and b is the slope of the line.