F4 Maths

圖片參考：https://s.yimg.com/lo/api/res/1.2/ZQit8r6YM3UMER1bF6V.OQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://i.imgur.com/ZH9B85L.gif

匿名 網友您好～

Quadratic Equation in One Unknown
1. The roots of equation 3x² + kx - 4k = 0, where k is a constant, are equal.
(a) Find the possible value(s) of k.
Double roots ⇒ Δ = 0
k² - 4(3)(-4k) = 0
k² + 48k = 0
k(k + 48) = 0
k = 0 or k = -48

(b) For each value of k, solve the above equation.
For k = 0, the equation is
3x² = 0
x² = 0
x = 0 (repeated)
For k = -48, the equation is
3x² - 48x + 192 = 0
x² - 16x + 64 = 0
(x - 8)² = 0
x = 8 (repeated)


Functions and Graphs
1. It is given that the graph of y = ax² + (a-3)x + 4 passes through A(-2, 6). Find the value of a.
Put x = -2 and y = 6 into the equation.
6 = a(-2)² + (a-3)(-2) + 4
6 = 4a - 2a + 6 + 4
2a = -4
a = -2

2. Find the x- and y-intercepts of the graph of y = (6 + 3x)/2.
Put y = 0,
6 + 3x = 0
3x = -6
x = -2 is the x-intercept.
Put x = 0,
y = (6 + 0)/2 = 3 is the y-intercept.


圖片參考：https://s.yimg.com/lo/api/res/1.2/cBSBlR.U.s7WswrSv8SArw--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://www.stormmediagroup.com/upload/frontend/de64aa90-6c17-431f-bf5d-97c0a71ad961/8f7ceb9f-db94-48ee-98f9-0a2f4bf1792a.gif


2014-08-07 17:20:59 補充：
辛苦 郭老 了~

我剛才答題時不知道您在這邊提意見~

Thanks!

double root when Δ = 0

k² - 4(3)(-4k) = 0
k² + 48k = 0
k = 0 or k = -48

x = (-k ± √Δ) / 2(3)

= 0 when k = 0
= 8 when k = -48

2014-08-07 17:13:39 補充：
1. It is giventhat the graph of y=ax²+(a-3)x+4 passes through A(-2, 6).Find the value of a.

6 = a(2)² + (a-3)(2) + 4
6 = 4a + 2a - 6 + 4
6 = 6a - 2
8 = 6a
a = 4/3

2014-08-07 17:15:20 補充：
2. Find the x- and y-intercepts of the graph of y=(6+3x)/2

when y = 0;

y=(6+3x)/2

0 = 6+3x

-6 = 3x

x = -2

x-intercept = -2

2014-08-07 17:16:13 補充：
when x = 0;

y=(6+3x)/2

y = 6/2 = 3

y-intercept = 3

2014-08-07 19:08:00 補充：
我計錯了 Functions and Graphs 的 (1)

睇錯了為 x = 2，Master 的答案才是正確的。