Strategically selecting values for t and plotting corresponding y values, you can create a linear segment of a quadratic function that appears as a straight line on a Cartesian graph.
The function y = 3t^2 + 4 is a quadratic equation, and quadratic functions typically produce a curve when graphed on a Cartesian plane. However, to create a straight line, it's essential to choose specific values for t and y that satisfy the equation.
If you set t=0, the equation simplifies to y=4, giving you the y-intercept. Similarly, if you set t=1 or t=−1, you get y=7, providing two more points on the graph. Connecting these points will form a straight line since they are linearly related. In this case, the graph starts at the point (0, 4) on the y-axis and passes through points (1, 7) and (-1, 7).
The key to understanding why this produces a straight line lies in the fact that the power of t in the equation is 2. When the power of t is 2, the graph typically forms a parabola, but by choosing specific values and connecting them, you can create a linear segment that mimics a straight line within the chosen interval. The result is a line segment that approximates the behavior of a straight line within that specific range of t values.