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Tcecarenko [31]
3 years ago
15

Formulate the quadratic function that contains the points (-2,1), (0,1) and (1,4).

Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
5 0
Y=ax^2+bx+c
when x=-2, y=1: 1=4a-2b+c
when x=0, y=1: 0x^2+0b+c=1 =>c=1
when x=1, y=4: 1a+1b+c=4, because c=1, a+b=3
back to x==-2, y=1, plugc=1 in the equation, 4a-2b=0
solve the system equation: a+b=3
                                            4a-2b=0
a=1, b=2
so the quadratic equation is: x^2+2x+1=0
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What is the cube root of -729
Ksju [112]

Answer:

-9

Step-by-step explanation:

-9 x -9 x -9 = -729

-9 x -9 = 81 x -9 = -729

8 0
3 years ago
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A motorist traveled 250 miles on 11 gallons of gas. With the same vehicle, about how far could he go on 16 gallons of gas? A) 17
Andrei [34K]
ANSWER

363.6 \: miles
EXPLANATION

We were told that the motorist travelled 250 miles on 11 gallons of gas. This implies that,

250 \: miles \equiv11 \: gallons

Now we want to find how far he could go on 16 gallons.

x \: miles \equiv16 \: gallons


All other things being equal, the motorist should cover more than 250 miles with 16 gallons of gas.

Recall that: If more, less divides.

This implies that,

x =  \frac{250 \times 16}{11}




x =  \frac{4000}{11}   = 363.6 \: miles


Therefore the correct answer is C.

3 0
4 years ago
Only need to answer question 1 but if you can pls answer both
algol [13]
Use the app photo map
5 0
4 years ago
The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).
garri49 [273]

Answer:

(-1,-6)

Step-by-step explanation:

f(x)=x^2+6x+3

g(x)=f(x-2)

g(x)=(x-2)^2+6(x-2)+3  (Replaced x in f with (x-2))

g(x)=x^2-4x+4+6x-12+3 (Used (x+b)^2=x^2+2bx+b^2 and distributive property)

g(x)=x^2-4x+6x+4-12+3 (Gathered like terms)

g(x)=x^2+2x-5  (Simplified)

The vertex of a parabola occurs at (\frac{-b}{2a},g(\frac{-b}{2a}).

Let's find \frac{-b}{2a} first.

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Now we can obtain g(\frac{-b}{2a}) which is g(-1) in this case:

g(x)=x^2+2x-5

g(-1)=(-1)^2+2(-1)-5

g(-1)=1-2-5

g(-1)=-1-5

g(-1)=-6.

The vertex is (-1,-6).

6 0
3 years ago
Ruby red paint costs $0.50 per square inch. A ball is painted ruby red and costs $100.00 to paint. What is the diameter of the b
8090 [49]
The diameter can be obtained by the formula A = pi*r^2

First, multiply 0.50 * 100 to obtain the area of the ball, then simplify and solve for the radius. Doubling the radius would yield the diameter. This is shown below:

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Among the choices, the correct answer is C. 8.0 in. 

6 0
3 years ago
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