Hi there!
Looking at the graph, the first intersection point is clear. The red parabola and blue line clearing intersect at the point (0, -1).
Find the second intersection point by setting the equations of both graphs equal to each other.
Line: y = 3x - 1
Parabola: y = 4x² - 1
Find another intersection point by setting these two equations equal to each other:
4x² - 1 = 3x - 1
Bring all terms onto one side:
4x² - 3x = 0
Factor out x:
x(4x - 3) = 0
Set 4x - 3 to 0 and solve:
4x - 3 = 0
4x = 3
x = 3/4
Plug in this value of x into an equation to solve for the y-coordinate. Use the linear equation for ease:
y = 3(3/4) - 1
y = 9/4 - 1
y = 5/4
(3/4, 5/4)