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Write an equation with the smallest possible degree for the function graphed above.
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Q. Write an equation with the smallest possible degree for the function graphed above.
- Identify key features: Identify the key features of the graph, such as -intercepts, -intercepts, turning points, and end behavior.
- Assume x-intercepts: Assume the graph has x-intercepts, which means the smallest possible degree is .
- Form factors from -intercepts: Use the -intercepts to form the factors of the polynomial. If the -intercept is at , then the factor is .
- Multiply factors for polynomial: Multiply the factors together to get the polynomial equation. If there are factors, the polynomial will be of degree .
- Check for y-intercept: Check if the graph passes through the origin, which would indicate a y-intercept at . If so, include this in the equation.
- Adjust leading coefficient: Adjust the leading coefficient to match the end behavior of the graph. If the graph goes up to the right, the leading coefficient should be positive; if it goes down to the right, the leading coefficient should be negative.
- Write final polynomial equation: Write down the final equation of the polynomial with the smallest possible degree that matches the graph.
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