math mix sensation(2) q4-5

Wallis

2014-10-31 4:59 am

4. It is given that V(2,5) is the vertex of the graph of a quadratic function y=f(x) .If f(4)=17,find
(a)f(x)
(b) the y-int of the graph

5. There exists a graph y=(k-1)x+2k where k is larger than 1 .It cuts the x-axis and the y-axis at pts A and B respectively, if the area of triangle AOB is 9 sq.units ,find all the possible values of k.

更新1:

any shorter steps for 4.? its too long i aim.fast in exam

更新2:

thanks!

更新3:

and also for no.5, how can u find the coordinates of A?

更新4:

looking to your reply��

回答 (1)

用戶10012

2014-10-31 3:15 pm

✔ 最佳答案

4.
Let y = f(x) = ax^2 + bx + c
f(4) = 16a + 4b + c = 17 ............(1)
V(2,5) is on the graph, so
5 = 4a + 2b + c ....................(2)
The x - coordinate of the vertex is - b/2a, so
2 = - b/2a
4a + b = 0 ..............(3)
(1) - (2)
12a + 2b = 12............(4)
(4) - (3) x 2
4a = 12
a = 3
From (3), b = -4a = - 12
Sub into (2)
5 = 12 - 24 + c
c = 5 + 12 = 17
so f(x) = 3x^2 - 12x + 17
(b) y intercept = f(0) = 17.
5.
For y = (k - 1)x + 2k
A is [ - 2k/(k - 1), 0 ], B is [ 0, 2k ]
OA = 2k/(k - 1), OB = 2k [ Note : OA is not -2k/(k - 1)]
Area of AOB = OA x OB/2 = 2k^2/(k - 1)
so 2k^2/(k - 1) = 9
2k^2 - 9k + 9 = 0
(2k - 3 )(k - 3) = 0
k = 3/2 or 3.

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