Suppose that equation of parabola is
y =ax² + bx + c
Since parabola passes through the point (2,−15) then
−15 = 4a + 2b + c
Since parabola passes through the point (-5,-29), then
−29 = 25a − 5b + c
Since parabola passes through the point (−3,−5), then
−5 = 9a − 3b + c
Thus, we obtained following system:
4a + 2b + c = −15
25a − 5b + c = −29
9a − 3b + c = −5
Solving it we get that
a = −2, b = −4, c = 1
Thus, equation of parabola is
y = −2x²− 4x + 1
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Rewriting in the form of
(x - h)² = 4p(y - k)
i) -2x² - 4x + 1 = y
ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)
iii) -3x² - 7x - 49/36 = y - 1 - 49/36
(Adding -49/36 to both sides to get perfect square on LHS)
iv) -3(x² + 7/3x + 49/36) = y - 3
(Taking out -3 common from LHS)
v) -3(x + 7/6)² = y - 445/36
vi) (x + 7/6)² = -⅓(y - 445/36)
(Shifting -⅓ to RHS)
vii) (x + 1)² = 4(-1/12)(y - 445/36)
(Rewriting in the form of 4(-1/12) ; This is 4p)
So, after rewriting the equation would be -
(x + 7/6)² = 4(-⅛)(y - 445/36)
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I hope this is what you wanted.
Regards,
Divyanka♪
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The image of the histogram distribution is missing, so i have attached it.
Answer:
Option C: The distribution is unimodal. Its mode is near 60 inches
Step-by-step explanation:
Mode simply means the most occurring value in a set of data.
Now, for histogram, the mode is the highest peak represented in the bars.
Now, from the image attached, it is seen that there is a clear highest peak. Thus, the histogram has only one peak and it can be described as unimodal.
We are not given the mode height from the histogram but we can see that it is between 60 and 68 inches. And if carefully observed it will have a value closer to 60.
Thus,option C is correct.
Answer: The initial height of the ball is 12 feet.
Step-by-step explanation:
We have the function
, which models the height (in feet) of the ball after
seconds.
Then, as the height is in function of the time, we know that the ball is in the initial height when:

So, to find the initial height, you need to substitute
into the function:

Therefore, the initial height of the ball is 12 feet.
Answer:
10 feet
Step-by-step explanation:
a²+b²+=c²
a=8ft
b=6ft
Answer:
It is open if it is greater or less than >
It is closed if it is greater than or equal to or less than or equal to > (but with the line underneath it)
Step-by-step explanation: