Respuesta :
The points of intersection are at (3, 6) and (-1, -2).
Since both of these equations have y isolated, we can set them equal to each other:
2x=x²-3
We want all of the variables on one side, so subtract 2x:
2x-2x = x²-3-2x
0=x²-3-2x
Write the quadratic in standard form:
0=x²-2x-3
This is easily factorable, as there are factors of -3 that will sum to -2. -3(1)=-3 and -3+1=-2:
0=(x-3)(x+1)
Using the zero product property we know that either x-3=0 or x+1=0; therefore x=3 or x=-1.
Substituting this into the first equation (it is simpler):
y=2(3) = 6
y=2(-1)=-2
Therefore the coordinates are (3, 6) and (-1, -2).
Since both of these equations have y isolated, we can set them equal to each other:
2x=x²-3
We want all of the variables on one side, so subtract 2x:
2x-2x = x²-3-2x
0=x²-3-2x
Write the quadratic in standard form:
0=x²-2x-3
This is easily factorable, as there are factors of -3 that will sum to -2. -3(1)=-3 and -3+1=-2:
0=(x-3)(x+1)
Using the zero product property we know that either x-3=0 or x+1=0; therefore x=3 or x=-1.
Substituting this into the first equation (it is simpler):
y=2(3) = 6
y=2(-1)=-2
Therefore the coordinates are (3, 6) and (-1, -2).
Answer:
Step-by-step explanation:
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
⇒ -3,
⇒ 0.59,
⇒ 3.41
