At which points are the equations y=x^2+3x+2 and y=2x+3 approximately equal?

(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).

24 units

step-by-step explanation:

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