SOLUTION: The parabola y=x2-4 intersects the x axis at two points, P and Q. What is the distance from P to Q?

Question 120433: The parabola y=x2-4 intersects the x axis at two points, P and Q. What is the distance from P to Q?
Found 2 solutions by josmiceli, bucky:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

set to find roots

The x-intercepts are the values of x that solve this

So, and
The distance apart is
answer
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given: the parabola
.

.
To find the intersections with the x-axis, set y = 0 because any point on the x-axis has
zero as its y-value. So the equation to solve then becomes:
.

.
Solve this by getting rid of the -4 on the right side by adding +4 to both sides. On the right
side the -4 and the +4 cancel each other when they are added. So when you add +4 to both sides
the equation becomes:
.

.
Solve for x by taking the square root of both sides to get two answers:
.
and
.
So the intersections of the parabola and the x-axis occur on the x-axis at x = -2 and at
x = +2. These points are P and Q. And, if you subtract them you get:
.

.
The points P and Q are 4 units apart.
.
You can see this in the graph of the parabola shown below:
.

.
Hope this helps you to understand the problem.
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