Final answer:
A translated parabola from y = x² - 3x + 4 has the form y = (x-h)² - 3(x-h) + 4 + k. The coefficients a and b in the equation y = ax + bx², representing projectile motion, depend on gravity and initial velocities.
Step-by-step explanation:
The equation of a parabola that is a translation of y = x² - 3x + 4 involves shifting the graph horizontally and/or vertically. The general form of the translated parabola will be y = (x-h)² - 3(x-h) + 4 + k, where h and k are the horizontal and vertical shifts respectively. For example, if we translate the parabola 2 units to the right and 3 units up, the new equation will be y = (x-2)² - 3(x-2) + 4 + 3. To find the equation of a parabola representing the trajectory of a projectile, you can use the horizontal distance (x) and the initial velocity components (Vox and Voy) to express time (t), and then substitute it into the vertical motion equation to obtain a form of y = ax + bx², where a and b are constants derived from acceleration due to gravity (g) and the initial velocities.