Jasminelane6478
26.07.2019 •
Mathematics
At which points are the equations y=x^2+3x+2 and y=2x+3 approximately equal?
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Ответ:
(0.618,4.236) and (-1.618,-0.236)
Step-by-step explanation:
To find the intersection, we are looking for a common point between the curves.
We are solving the system:
.
I'm going to do this by substitution:
Subtract 2x and 3 on both sides:
To solve this equation I'm going to use the quadratic formula:
To find , you must compare
to .
.
Now inputting the values into the quadratic formula gives us:
This means you have two solutions:
It does say approximately.
So I'm going to put both of these in my calculator and I guess round to the nearest thousandths.
Now to find the corresponding y coordinates, I need to use one the equations along with each x.
I choose the linear equation: y=2x+3.
y=2x+3 when x=0.618
y=2(0.618)+3=4.236
So one approximate point is (0.618,4.236).
y=2x+3 when x=-1.618
y=2(-1.618)+3=-0.236
So another approximate point is (-1.618,-0.236).
Ответ: