Question

The height of Amelia's mid-section was measured three times during a long jump.

Time in seconds, x 0 0.5 1
Height in meters, y​ 0.7​ 1.5​ 0.55​​

Write the equation of a quadratic function that describes Amelia's height as a function of time.

Answer 1

The equation of the quadratic function that describes Amelia's height as a function of time is y = -0.7x^2 + 0.55x + 0.7.

Step-by-step explanation:

To write the equation of a quadratic function that describes Amelia's height as a function of time, we can use the formula y = ax^2 + bx + c, where a, b, and c are constants. We have three sets of data points: (0, 0.7), (0.5, 1.5), and (1, 0.55). We can substitute these values into the equation and solve for the constants. Using the first point (0, 0.7), we get the equation 0.7 = a(0)^2 + b(0) + c, which simplifies to c = 0.7. Using the second point (0.5, 1.5), we get the equation 1.5 = a(0.5)^2 + b(0.5) + 0.7, which simplifies to 0.25a + 0.5b = 0.8. Using the third point (1, 0.55), we get the equation 0.55 = a(1)^2 + b(1) + 0.7, which simplifies to a + b = -0.15. Solving these two equations simultaneously, we find that a = -0.7 and b = 0.55. Therefore, the equation of the quadratic function that describes Amelia's height as a function of time is y = -0.7x^2 + 0.55x + 0.7.