Question

:)

Answer 1

9.5 is correct.

(ii) (1) Find the coordinates of the point where the line x = -10 meets the parabola.
What will be the x-coordinate of the point where they meet? Remember, the point is on BOTH graphs: y= -0.03x^2 + 0.03x + 9.5 AND x = -10.

Answer 2

Can you answer my previous question?

Answer 3

The x-coordinate of the point of intersection will be -10.
The y-coordinate can be found by substituting x = -10 in y= -0.03x^2 + 0.03x + 9.5. y = -0.03(-10)^2 + 0.03(-10) + 9.5 = -3 - 0.3 + 9.5 = 6.2

Point of intersection: (-10, 6.2)

Answer 4

(2) "...10 cm to the left of the centre line of the photo...."
requires us to first find the centre line or the axis of symmetry of the parabola.
Can you find the axis of symmetry?

Answer 5

In this case the axis of symmetry or the centre line will be a vertical line that passes through the vertex of the parabola.

Answer 6

All we need is the x-coordinate of the vertex of the parabola.

Answer 7

Oh, never mind. Reread the problem. x is measured from the center line (not typical) and so x = 0 is the center line.

Answer 8

Well, that would be the vertex in the typical case. But here they have shifted the y axis to the right by 0.5 units to make the y-axis the center line. So x = 0 is the center line. In typical cases x = 0.5 would be the center line but not here.

Answer 9

I think there is an error in the problem statement (just off by a small amount).

Answer 10

The way the equation is stated: y= -0.03x^2 + 0.03x + 9.5, the center line is at x = 0.5. But they say the x values are measured from the center line in which case they have moved the y-axis to the right by 0.5 units to coincide with the center line. But that would change the equation of the parabola. So there is an error (even though a small error going from from x = 0 to x = 0.5. But still an error).

Answer 11

But we can still answer the problem correctly despite their small error in problem statement because they say: "Use your answer to part (d)(ii)(1) to explain whether the rainbow is above or below the mountain peak."
In part d(ii)(1) we got the coordinates as (-10, 6.2)
Since 6.2 cm is greater than the mountain peak at 5 cm, the rainbow is ABOVE the mountain peak.

Answer 12

But despite the error in the part (indicated in bold) "where x is the horizontal distance .... FROM THE CENTRE LINE of the photo." it is fairly easy to answer the rest of the questions.

Answer 13

They want the answer to one decimal place. So the x-intercepts are: -17.3 and 18.3

Answer 14

(d)(iii)(2): The width of the rainbow at its widest part is basically how far apart the x-intercepts are. 18.3 - (-17.3) = 35.6 cm.

Answer 15

You are welcome.