Which of the following points are on the graph of y2 x3 x4

Which of the following points are on the graph of y^2 = x^3 - x+4 ? (-2, squareroot 2) (1, 2) (-3 squareroot 20) (0, 2) (2, squareroot 10) (-1, -2)

Solution

given curve y²=x³-x+4

testing each point in the given equation

(1)

(x,y)=(-2,2)

(2)²=(-2)³-(-2)+4

2=-8+2+4

2=-2 -----> not true

so (-2,2) is not on the graph of  y²=x³-x+4

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(2)

(x,y)=(1,2)

(2)²=(1)³-(1)+4

4=1-1+4

4=4 -----> true

so (1,2) is on the graph of  y²=x³-x+4

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(3)

(x,y)=(-3,20)

(20)²=(-3)³-(-3)+4

20=-27+3+4

20=-20 -----> not true

so (-3,20) is not on the graph of  y²=x³-x+4

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(4)

(x,y)=(0,2)

(2)²=(0)³-(0)+4

4=0-0+4

4=4 -----> true

so (0,2) is on the graph of  y²=x³-x+4

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(5)

(x,y)=(2,10)

(10)²=(2)³-(2)+4

10=8-2+4

10=10 -----> true

so (2,10) is on the graph of  y²=x³-x+4

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(6)

(x,y)=(-1,-2)

(-2)²=(-1)³-(-1)+4

4=-1+1+4

4=4 -----> true

so (-1,-2) is on the graph of  y²=x³-x+4

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points on graph are (1,2),(0,2),(2,10),(-1,-2)