I can't figure this outthis question was on my exam and I got it completely wrong
(I have a graphing calculator capble of matrices so yo don't have to solve the system of equations by hand, use rref (reduced row echelon form))
values of a, b, and c and the equation of the graph of the parabola
y=ax^2+bx+c
such that is passes through the points
(2,-15)
(-5,-29)
(-3,5)
rewrite it in the form (x-h)^2=4P(y-k)
show all work
if I were to sub the points in I would ge
(2,-15): -15=4a+2b+c
(-5,-29): -29=25a-5b+c
(-3,5): 5=9a-3b+c
then solve for a, b and c
I don't know how to solve, please help
(if I don't undestand your answer, I will either report or ask you to explain more)
Answers
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
____________________
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)
__________________
I hope this is what you wanted.
Regards,
Divyanka♪
__________________
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 = −3, b = −7, c = 11
Thus, equation of parabola is
y = −3x²− 7x + 11
____________________
Rewriting in the form of
(x - h)² = 4p(y - k)
i) -3x² - 7x + 11 = y
ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)
iii) -3x² - 7x - 147/36 = y - 11 - 147/36
(Adding -147/36 to both sides to get perfect square on LHS)
iv) -3(x² + 7/3x + 49/36) = y - 543/36
(Taking out -3 common from LHS)
v) -3(x + 7/6)² = y - 181/12
vi) (x + 7/6)² = -⅓(y - 181/12)
(Shifting -⅓ to RHS)
vii) (x + 1)² = 4(-1/12)(y - 181/12)
(Rewriting in the form of 4(-1/12) ; This is 4p)
So, after rewriting the equation would be -
(x + 7/6)² = 4(-1/12)(y - 181/12)
_________________
I have corrected the answer and wrote again since the time to correct the answer from that account was expired.
- Divyanka
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2.It must be a positive number since it represents a number of hours.
3. It must be a negative number because the depth is below sea level.
4.It cannot be greater than –72 because that is the depth of the well.
Answers
Answer:
Option B is correct
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As per the statement:
Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.
Given the equation as:
Using distributive property,
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Subtract 40 from both sides we have;
Divide both sides by -8 we have;
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Answers
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25
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Answers
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x = 1800/25
x = 72
So, option D is your answer.
Hope this helps!
Answer:
d
Step-by-step explanation:
Answers
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Answers
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