A parabola has x-axis intercepts 6 and -3, and passes through the point (1,10). Find the equation of the parabola.
1 answer:
Answer:
y=-1/2 x^2+3/2 x+9
Step-by-step explanation:
The equation of parabola is:
y=ax^2+bx+c
We know that parabola has three poibts
(6,0),(-3,0) and (1,10).
So we put these three points in equation:
a*36+b*6+c=0......(1)
a*9-3b+c=0........(2)
a+b+c=10........(3)
(1)-(2) we have:
27a+9b=0.....(4)
(2)-(3) we have:
8a-4b=-10.....(5)
4(4)+9(5) we got:
180a=-90
a=-1/2
From (4) we got: b=27/18=3/2
From (3) we got: c=10+1/2-3/2=9
So equation is:
y=-1/2 x^2+3/2 x+9
You can see the picture of parabola through three points.
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now, let's check when they're both equal, at how many hours will they cost your sister the same amount.
so, 3 and a third of a hour, or 3 hours and 20 minutes, they both will cost your sister the same amount, so it wouldn't matter who's hired if the party is only 3 hours and 20 minutes long.
however, after that, the one with higher hourly rate, Marvin's, gets more expensive, and she's better off hiring the one with cheaper hourly rate.
now, you can just get some mp3s and some loud speakers and nevermind the DJs and you do it, or she can do it, I have the macarena song if you need that one.