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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Y=Mx+b
M=3
Now you need b, so plug the x-coordinate and y-coordinate into the x and y in the equation to find the b.
-5=3(-3)+b
-5=-9+b
Add 9 to both sides to isolate the b
-5=-9+b
+9. +9
4=b
So the equation is
Y=3x+4
<span>4x = −4
</span>
Question 2
<span> 2(2x − 5 − 4) = 160 − 17
4x-10-8 = 160-17
4x-18=143
4x = 161
x=40.25
</span>
Question 3
<span>4(2z + 3) = 12
8z +12 = 12
8z = 0
z = 0
</span><span>Question 4
</span>
<span>5(2x − 6) + 20 = 10
10x-30+20=10
10x-10=10
10x =20
x=2
</span>
<span>Question 5
</span>
<span>5x + 10 = 5x − 8
5x+18=5x
18=0
Zero solutions
</span>
The answer to the question is a
Answer:
1. 3 2
/5
2. 2/
3
3. 3/4
Step-by-step explanation:
