f'ns and transformations

[nacho]

Hi,
These are out of the year 12 maths quest book, pages 64 - 65:

11. For the parabola whos range is y <= 3, whose x-coordinate of the turning point is -4 and whose y-intercept is y = -2 1/3, find:

a. the y-coordinate of the turning point
b. the equation of the parabola
c. the coordinates of the x-intercepts

[kaushik]

y = a(x − h)2 + k
a) Range is y ≤ 3 ⇒ a < 0
   and k = 3 is the y-coordinate of
   turning point.
   h = −4

edit i can't do the others without latex. how do i use latex? 

[xZero]

a.the given range should tell you that the parabola is reflected in the x-axis and the highest value within the range should be the y-coordinate of the turning point y=3

b.the general form of a parabola is
then differentiate the equation to get , since the turning point is at , we can sub it into the derivative to get 

sub into so you get , then sub and into the equation to find a, then you can find b from there

c. should be straight forward

this was under the assumption that the parabola was inverted, someone verify my working please

[xZero]

y = a(x − h)2 + k
a) Range is y ≤ 3 ⇒ a < 0
   and k = 3 is the y-coordinate of
   turning point.
   h = −4

edit i can't do the others without latex. how do i use latex? 

http://vce.atarnotes.com/forum/index.php/topic,3137.0.html

[nacho]

b.the general form of a parabola is
then differentiate the equation to get , since the turning point is at , we can sub it into the derivative to get  

sub into so you get , then sub and into the equation to find a, then you can find b from there

thanks!
T_T can't believe i didn't realise question a...
Anyway, for b, is there another way? ALthough it's assumed knowledge, i feel MQuest isn't the type to ask a question in which calculus is involved, especially in ch. 2

[xZero]

b.the general form of a parabola is
then differentiate the equation to get , since the turning point is at , we can sub it into the derivative to get  

sub into so you get , then sub and into the equation to find a, then you can find b from there

thanks!
T_T can't believe i didn't realise question a...
Anyway, for b, is there another way? ALthough it's assumed knowledge, i feel MQuest isn't the type to ask a question in which calculus is involved, especially in ch. 2

well i did part b before i realised part a LOL but anyways use (T.P form), sub in to find a and viola, part B's done

Edit: apparently if you torrenting while posting you can triple post without knowing  

[pHysiX]

*voila