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deff fn [24]
3 years ago
7

2. f(x) = 3(x - 2)2 + 6a. Standard Form:​

Mathematics
1 answer:
Alexandra [31]3 years ago
6 0

Answer:

{3x}^{2}   - 4x + 10 = 0

Step-by-step explanation:

3(x - 2) {}^{2}  + 6 \\  3 \times x {}^{2}  - 4x +  {2}^{2}  + 6 \\ 3x {}^{2} - 4x + 4 + 6 \\  {3x}^{2}   - 4x + 10 = 0

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Find the point that is 1/5 the way from A to B where<br> A(-7,4) and B(3, 10).
mestny [16]

Answer:

The coordinates of the point that is 1/5 the way from A to B  is (x,y) = (-5,\frac{26}{5})

Step-by-step explanation:

Here, the given points are: A (-7,4) and B (3,10)

Let us assume  the point M(x,y) on AB is such that

AM : AB = 1 : 5

⇒ AM  : (AB - AM) = 1 : (5-1)  = 1: 4

⇒ AM  : MB  = 1 : 4

Now, The Section Formula states the coordinates of point (x,y) on any line dividing the line in the ratio m1 : m2

(x,y) = (\frac{m_2x_1+m_1x_2}{m_1+m_2} ,\frac{m_2y_1+m_1y_2}{m_1+m_2}  )

Here, in the given equation, m1: m2 = 1:4

So, the coordinates M(x,y) is given as:

(x,y) = (\frac{(-7)(4) + 1 (3)}{1+ 4} ,\frac{4(4) + 1(10)}{1+4}  )\\\implies (x,y) = (\frac{-28+3}{5} ,\frac{16+10}{5} )  = (\frac{-25}{5} ,\frac{26}{5} )\\\implies (x,y) = (-5,\frac{26}{5} )

Hence, the coordinates of the point that is 1/5 the way

from A to B  is (x,y) = (-5,\frac{26}{5})

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