Answer:
591
Step-by-step explanation:
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
____________________
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♪
__________________
Well... hell, let's just convert them all with the same denominator then
hmmm let's see, we have the denominators of 8,11 and 3
so... we'll multiply the 5/8 times (11*3) or 33
and then we'll multiply 7/11 times (8*3) or 24
and then we'll multiply 2/3 times (8 * 11)
notice, we're simply using the other's denominator's product, to multiply the fractions... anyhow... let's check
The interval that represents the inequality 1 < x ≤ 6 is given by:
B. (1,6].
<h3>What is the standard interval notation?</h3>
The standard interval notation of an interval of lower bound a and upper bound b is given by:
[a,b].
The inequality notation is:
a ≤ x ≤ b
The set builder notation is:
{x | a ≤ x ≤ b}.
In this problem, we are given the inequality 1 ≤ x ≤ 6, hence a = 1 and b = 6, and <u>open at x = 1 and closed at x = 6,</u> hence the interval is:
B. (1,6].
More can be learned about intervals and inequalities at brainly.com/question/15034661
#SPJ1
