Question

41. Compare the parabola defined by each equation with the standard parabola defined by the equation y = x². Describe the corresponding transformations, and include the position of the vertex and the equation of the axis of symmetry.

y = 3x² - 8 (4 marks)

B. y = (x – 6)² + 4 (4 marks)

C. y = -4(x + 3)² - 7 (5 marks)

Answer 1

y = 3x² - 8 (4 marks)
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well that 3 makes it climb up three times as fast
now your original y = x^2 had a vertex at (0,0)
where is it for this one?
for every x, y is 8 less, so it is 8 units lower
vertex at (0,-8), symmetric about that vertical line through x = 0
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B. y = (x – 6)² + 4 (4 marks)
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y - 4 = (x-6)^2
well this time it will go up like the original but x = 6, y = 4, symmetric about x = 6 (note if x = 7, (7-6)^2 = 1 and if x = 5, (5-6)^2 = 1 :). The bottom will be at y = 4 (6,4)
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C. y = -4(x + 3)² - 7 (5 marks)
y+7 = -4 (x+3)^2
this opens down (sheds water) beause y goes to -oo when x gets big + or -
this tops when y = -7 and x = -3
it is 4 times as steep as the original

Answer 2

Thank you so much, I really appreciate it.

Answer 3

You are welcome.