when the solutions to each of the two equations below are graphed in the xy coordinate plane, the graphs of the solutions inters ect at two places. Write the y-coordinate of the points of intersection in the boxes below in order from smallest to largest. y=2x and y=x^2-3
2 answers:
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).
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
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