PLEASE HELP I BEG 70 POINTS Part A: Explain how to sketch the graph of a curve that opens downwards and has only one x-intercept at (2.5,0).

Part B: Explain how to sketch the graph of a curve that opens upwards where the minimum value of the graph is (0,1).

Part C: Explain how to sketch the graph of a curve with the following characteristics.
• The graph opens downward.
• The y-intercept is (0,6).
The z-intercepts are (-1,0) and (3, 0).
• The maximum value of the function is located at the point (1,8).

Part A:

If a quadratic has only one x-intercept, then that is where the vertex lies. being that the vertex is the highest or lowest point in the quadratic. To sketch, it will open downwards with a single x-cept

Part B:

The graph will be above the x-axis. And having the vertex being at (0,1) as it says its the minimum value. All the minimum means is that its the lowest value of this given parabola.

Part C:

Plot the points of the y-intercept and z-intercepts. Then plot the maximum value is. Connect the dots.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."