State whether the given equation represents a linear, quadratic, or exponential function. Tell how you decided.
y = -8x2 + 4
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linear
To determine whether the given equation represents a linear, quadratic, or exponential function, we need to analyze the form of the equation.
A linear function is an equation where the highest exponent of the variable is 1. It has the form y = mx + b, where m is the slope and b is the y-intercept.
A quadratic function is an equation where the highest exponent of the variable is 2. It has the form y = ax^2 + bx + c, where a, b, and c are constants.
An exponential function is an equation where the variable appears in the exponent. It has the form y = a*b^x, where a and b are constants.
In the given equation y = -8x^2 + 4, we can see that the highest exponent of the variable is 2 (x^2), which means it is a quadratic function. Therefore, the given equation represents a quadratic function.
To decide, we looked at the highest exponent of the variable in the equation, which was 2. This indicates a quadratic function.