Formula of the parabola: (x - h)²<span> = 4p(y - k)
(h,k) is a vertex, </span>(1,-9) is a vertex.
<span>h=1, k= - 9
Substitute h and k into formula </span>(x - h)² = 4p(y - k)
(x - 1)² = 4p(y + 9)
Substitute x and y of the y-intercept
(x - 1)² = 4p(y + 9), x=0,y=-6.
(0 - 1)² = 4p(-6 + 9)
1 = 4p*3
1/3 = 4p, substitute value of 4p into (x - 1)² = 4p(y + 9).
(x - 1)² = 1/3(y + 9)
x²-2x+1=(1/3)y + 3
(1/3)y = x²-2x-2
y = 3x² - 6x -6
x-intercepts, is values of x when y=0.
3x² - 6x -6 = 0
x²-2x-2=0
We will find values of x using formula.
Given
A laboratory technician needs to make a 117-liter batch of a 20% acid solution.
How much the technician combine an acid solution that is pure acid with another that is 10% to get the desired concentration.
To proof
let us assume that the solution that is pure acid = x liters
let us assume that the anthor solution that is 10% = y liters
Than
the equation becomes
x + y = 117
As given in the question
technician needs to make a 117-liter batch of a 20% acid solution
laboratory technician combine an acid solution that is pure acid with another that is 10% to get the desired concentration
Convert 20% in the simpler form
= 0.2
Convert 10% in the simpler form
= 0.1
Than the equation becomes
0.2 × 117 = x + 0.1y
234 = 10x + y
Than the two equation are
x + y = 117
234 = 10x + y
subtracted x + y = 117 from 234 = 10x + y
10x+y -x -y = 234 -117
9x = 117
x= 13
put this in the equation x + y = 117
13 + y =117
y = 117 - 13
y = 104
Therefore
The solution that is pure acid be 13 liters.
than the other solution that is 10% is 104 liters.
Hence proved
Answer:
-28(x + 2) = (y - 1)²
Step-by-step explanation:
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