Question

Find the length of the segment AB if points A and B are the intersection points of the parabolas with equations y=−x2+9 and y=2x2−3 . URGENT PLS HELP

Answer 1

The length is 4

Explanation:

Type in the equations into Desmos, and you will find the intersected points in the graph. Then just look at the distance between the 2 points

Answer 2

AB=4

Explanation:

1. Since you are finding the intersection points of two parabolas:

a. y=-x²+9

b. y=2x²-3

2. You have to set them equal to each other:

2x²-3= - x²+9

2x²+x=9+3

3x²=12

x²=4

This is the crucial part; the absolute value of x is equal to plus minus the square root of 4, since either -2 squared with parentheses or 2 squared is equal to 4.

√x²=±√4

x=±2

or

x=2; x=-2

3. Then you substitute them into each equation. For this step, any sign 2 will work.

a. y=-(2)²+9

y=-4+9

y=5

b. y=2(2)²-3

y=8-3

y=5

4. So our coordinates will be (2,5) and (-2,5). These are the points of intersection.

5. Now we use the distance formula:

`\sqrt{(x₂-x₁)^(2) +(y₂-y₁)^(2) }`

The subscripts didn't work for this but I mean the square root of x 2 - x 1 in parentheses plus y 2 -y 1.

`\sqrt{(2+2)^(2) +(5-5)^(2) }`=

√16=

4

The absolute value rule that I mentioned above doesn't work for this because its a distance and you can't have a negative distance.

So AB=4