This mathematics question involves graphing equations and using tools like the PhET Explorations: Equation Grapher to understand how polynomial curves are shaped. The student is provided steps to match a graph to its equation by identifying, ensuring correct units, and calculating the answer.
The subject of this question involves mathematics, specifically graphing and matching equations to their respective graphs. When matching a graph to its correct equation, a few steps need to be followed:
- Identify the equation that matches the characteristics of the graph such as the slope, y-intercept, or curvature.
- Confirm that all values are in the correct units before plugging them into the equation.
- Once values are plugged in, calculate the answer and ensure that the units are consistent throughout the solution.
For example, a linear equation will be a straight line, a quadratic equation will show a parabolic curve, and an exponential equation will show a J-shaped curve on a graph. To label and shade a graph properly, the x-axis and y-axis should be labeled, and the appropriate region shaded, such as the right tail for a distribution curve.
The PhET Explorations: Equation Grapher is a tool that can be used to learn about graphing polynomials and the effect of changing constants on the shape of a polynomial curve.