Solve the question, thank you
2 answers:
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Answer:
a) y = (x -4)² -4
b) (4, -4)
c) translated 4 right, 4 down
Step-by-step explanation:
a) Apparently "graphing form" is a reference to "vertex form." That form is ...
y = a(x -h)² +k . . . . . . parabola with vertex (h, k) and vertical scale factor 'a'
The coefficient of x² in your given equation is 1, so a=1. The values of h and k can be found as follows.
'h' is the opposite of half the x-coefficient in your equation, so is h = -(-8/2) = 4. The value of k is the square of h, subtracted from the constant in your equation: k = 12 -h² = 12 -16 = -4. (This applies when a=1, as here.) These calculations are the "cut to the chase" version of "completing the square."
The method of "completing the square" has you consider the x-terms separately from the constant term:
y = (x² -8x) +12
To "complete the square", you want to make the terms in parentheses be a perfect square trinomial. You do that by adding the square of half the x-coefficient. In order to keep the same equation, you need to subtract an equivalent amount outside parentheses:
y = (x² -8x +(-8/2)²) +12 -(-8/2)² . . . . . add and subtract (-8/2)²
y = (x -4)² +(12 -16)
Then the vertex form is ...
y = (x -4)² -4 . . . . and the vertex is (h, k) = (4, -4).
The graphing calculator plot attached confirms this vertex value.
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The problem statement tells you that you can also find this form by averaging the x-intercepts. If you factor your equation, you get ...
y = (x -6)(x -2)
The x-values that make these factors zero {6, 2} are the x-intercepts. Their average (6+2)/2 = 4 is the x-coordinate of the vertex (h). You can find the y-coordinate of the vertex by evaluating y when x=4: y = 4² -8·4 +12 = -4. So, the vertex by this method is (h, k) = (4, -4), and the equation in graphing form is ...
y = (x -4)² -4 . . . . as above.
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b) As we saw above, the vertex coordinates are (h, k) = (4, -4).
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c) The vertical scale factor 'a' is 1, so the only transformation done on the graph is to move the parent vertex (0, 0) to the location (4, -4). That is, the graph has been translated 4 units right and 4 units down. (In the attached, the parent function is shown with a dashed line.)
We are told that Carrie borrows $960 interest free to pay for a car repair. She will repay $120 monthly until the loan is paid off and we are asked to find how many months will it take Carrie to pay off the loan.
In order to find out the number of months to pay off the loan we will divide total amount borrowed by monthly loan installment.
Therefore, Carrie have to pay $120 for 8 months to payoff the loan.