The graphs of the pair of functions intersect. Find the x-coordinates of the points of intersection without using a calculator and show your steps.(Hint: Solve as a system using substitution.)
y = x^2 - 3
y = 4x^2 - 12x - 3
To find the x-coordinates of the points of intersection, we need to set the two equations equal to each other:
x^2 - 3 = 4x^2 - 12x - 3
Subtracting 4x^2 and adding 12x on both sides gives us:
0 = 3x^2 - 12x
Now we can factor out the common factor of 3x:
0 = 3x(x - 4)
Setting each factor equal to zero gives us two possible solutions:
3x = 0 --> x = 0
x - 4 = 0 --> x = 4
Therefore, the x-coordinates of the points of intersection are x = 0 and x = 4.