The line y=16x intersects the quadratic function y=x^2 at two points. What are the coordinates of the two points of intersection?
To find the coordinates of the points of intersection between the line y = 16x and the quadratic function y = x^2, we need to set the two equations equal to each other and solve for x.
Setting y = 16x equal to y = x^2:
16x = x^2
Bringing all terms to one side, we have:
x^2 - 16x = 0
Now, we can factor out an x:
x(x - 16) = 0
So, we have two possibilities:
1. x = 0
2. x - 16 = 0
Solving for x in the first case:
x = 0
In the second case:
x - 16 = 0
x = 16
Therefore, the two points of intersection are (0, 0) and (16, 256).
To find the coordinates of the points of intersection between the line y = 16x and the quadratic function y = x^2, we need to set the two equations equal to each other and solve for x.
1. Set the equations equal to each other:
16x = x^2
2. Rearrange the equation by bringing all terms to one side to form a quadratic equation:
x^2 - 16x = 0
3. Factor out x from the equation:
x(x - 16) = 0
4. Apply the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero. Thus, set each factor equal to zero and solve for x.
Factor 1:
x = 0
Factor 2:
x - 16 = 0
x = 16
Therefore, the two points of intersection between the line y = 16x and the quadratic function y = x^2 are (0, 0) and (16, 256).
16 x = x^2
x^2 -16 x = 0
x(x-16) = 0
x = 0 or x = 16
y = 0 or y = 256
(0,0) and (16 , 256)