The upward opening parabola f of x vertex is at (0, 0) with the left and right slopes pass through (negative 2, 4) and (2, 4) in quadrants 2 and 1. The upward opening parabola g of x vertex is at (0, 0) with the left slope passing through (negative 2, 2) in quadrant 2 and the right slope passing through the plotted closed circle (2, 2) in quadrant 1.

Question

The upward opening parabola f of x vertex is at (0, 0) with the left and right slopes pass through (negative 2, 4) and (2, 4) in quadrants 2 and 1. The upward opening parabola g of x vertex is at (0, 0) with the left slope passing through (negative 2, 2) in quadrant 2 and the right slope passing through the plotted closed circle (2, 2) in quadrant 1.

f(x)=x^2 what is gx?

Answer 1

Given that the vertex of g(x) is at (0, 0) and the left slope passes through (-2, 2) and the right slope passes through (2, 2), we can deduce that the equation of g(x) is also a parabola with its vertex at (0, 0).

Since the vertex is at (0, 0), the equation of g(x) can be written in the form g(x) = ax^2.

To find the value of a, we can use the point-slope form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept.

For the left slope, passing through (-2, 2):
2 = (-2)a
a = -1

For the right slope, passing through (2, 2):
2 = (2)a
a = 1

Since both slopes should give the same value for a, it is not possible to have different values of a for the left and right slopes. Therefore, there is a contradiction in the provided information, and a valid equation for g(x) cannot be determined without additional information or clarification.