1: For each equation, complete the table of values and draw its graph for values of \( x \) from -1 to 3 .

If we take a simple quadratic equation like \( y = x^2 \) for our values of \( x \) from -1 to 3, we can generate some fun and engaging pairs to fill in the table. For example: - When \( x = -1 \), \( y = (-1)^2 = 1 \) - When \( x = 0 \), \( y = 0^2 = 0 \) - When \( x = 1 \), \( y = 1^2 = 1 \) - When \( x = 2 \), \( y = 2^2 = 4 \) - When \( x = 3 \), \( y = 3^2 = 9 \) Pop all those values in a table, and you've got the points: | \( x \) | \( y \) | |:---------:|:---------:| | -1 | 1 | | 0 | 0 | | 1 | 1 | | 2 | 4 | | 3 | 9 | Plot those points and connect them smoothly to see a charming upward-opening parabola! Want some extra excitement? Did you know that the concept of graphing equations dates back to the 17th century? René Descartes, a dazzling mind, laid out the foundation of coordinate geometry. He showed how algebra can beautifully converge with geometry, revolutionizing math! And let’s not forget about the real-world applications of graphing equations! From physics to economics, nearly any field can use graphing to visualize equations. Ever wanted to model the trajectory of a thrown ball or the growth rate of a population? Graphs turn abstract numbers into visual stories, making data easier to digest and decisions easier to make!