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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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7 1/8 is greater than 7.025 because if you convert it into a decimal (8 * 7 = 56 + 1 = 57/8 =....) you get 7.125, which is obviously bigger (1>0)
Answer:
Point on Midline (0,3)
Maximum (9π/2,3)
Minimum (-9π/2,-3)
Step-by-step explanation:
in the given sine function which is in the form of f(x) = a sin(bx+c) +d
a = amplitude
period = frequency = 18π
Therefore b = 2π/18π = 1/9
Y intercept = vertical shift = 3
Horizontal shift = d = 0
Therefore the sine function will be
f(x) = 6 sin(x/9) + 3
Now first point on the midline is (0,3)
Second point is maximum (9π/2,9)
Third point be a minimum value ( -9π/2,-3)
