Describe the transformation of f{x) = x? represented by g. Then graph each function. 1. 2. 3. gx)=(x+972+7 g(x) = 5x> + 0.75 Let the graph of g be a vertical shrink by a factor of 0.25 and a reflection in the x-axis, followed by a translation 2 units right of the graph of f(x) = x2. Write a rule for g and identify the vertex. . Let the graph of g be a translation 6 units right and 8 units up, followed by a reflection in the x-axis of the graph of f{x) = x2 4x. Write a rule for g. . The height h (in feet) of a water balloon after it is launched can be modeled by h(x) = 0.04x? + 0.4x + 3, where x is the horizontal distance (in feet) from the launch pad. The launch pad is adjusted so that the water balloon lands 5 feet farther from the launch pad. Write a function that models the new path of the water balloon. Graph the function. Label the vertex and axis of symmetry. 1. ix)=6(x 972 + 4 2. X)=x>+2x4 3. Find the minimum value or maximum value of f{x) = 3x? + 12x 4. Find the domain and range of the function, and when the function is increasing and decreasing. 4. The parabola shows the path of your first golf shot, where x is the horizontal distance (in yards) and y is the corresponding height (in yards). 0,0y The path of your opponent's first golf shot is modeled by the function g(x) = 0.04x(x 90). Which shot travels farther before hitting the ground? Which travels higher? . Write an equation of the parabola with focus F(0, 8) and directrix y=-8. . ldentify the focus, directrix, and axis of symmetry of 8y = x2. Graph the equation. 3. Write an equation of the parabola with vertex (0, 0) and directrix x = 6. 4. Write an equation of the parabola with vertex (2, 10) and focus (2, 9.5). 5. The parabolic cross section of an arch is 10 feet wide at ground level. Write an equation that represents the cross section of the arch with its vertex at (0, 0) and its focus 0.5 foot below the vertex. What is the height of the arch