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jonathanrgarcia
12.07.2021 •
Mathematics
Write an equation for a parabola that has a vertex (1, 2) and passes through the point (3, -6).
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Ответ:
y= -2x²+4x.
Step-by-step explanation:
the common equation of the parabola is y=ax²+bx+c, where a, b, c - numbers.
1) the coordinates of the vertex are:
2) if according to the condition x₀=1, then b= -2a.
If according to the condition y₀=2, then![2=\frac{4ac-b^2}{4a}=\frac{4ac-4a^2}{4a}=c-a;](/tpl/images/1392/5880/4e9b2.png)
it means that c=a+2.
3) if b= -2a; c=a+2 and the point (3;-6) belongs to the given parabola, then it is possible to substitute them into the common equation of the parabola:
-6=3²*a-6a+a+2; ⇔ a= -2.
4) if a= -2, then b=-2a=4, and c=a+2=0.
5) if a=-2, b=4 and c=0, then the required equation of the parabola is:
y= -2x²+4x.
Ответ:
1,200 cm3
Step-by-step explanation:
p = 2l + 2w
60 = 2(3x + 2) + 2(2x - 2)
60 = 6x + 4 + 4x - 4
60 = 10x
x = 6
Thus,
l = 3x + 2 = 3(6) + 2 = 20
w = 2x - 2 = 2(6) - 2 = 10
h = x = 6
V = lwh = (20)(10)(6) = 1,200 cm3