Question

What is the equation, in standard form, of a parabola that contains the following points? (1 point) Responses Image with alt text: y equals negative 2.5 x squared plus 5 x Image with alt text: y equals negative x squared plus 4 x minus 4 Image with alt text: y equals negative 2 x squared plus 4 x minus 4

Answer 1

The equation, in standard form, of a parabola that contains the given points can be determined by finding the coefficients that satisfy the equations.

1. For the first point (1, 5), substitute the values of x and y into the equation y = -2.5x^2 + 5x:
5 = -2.5(1^2) + 5(1)
5 = -2.5 + 5
5 = 2.5
This equation is not satisfied by the first point, so it is not part of the parabola.

2. For the second point (1, -4), substitute the values of x and y into the equation y = -x^2 + 4x - 4:
-4 = -(1^2) + 4(1) - 4
-4 = -1 + 4 - 4
-4 = -1
This equation is not satisfied by the second point, so it is not part of the parabola.

3. For the third point (1, -4), substitute the values of x and y into the equation y = -2x^2 + 4x - 4:
-4 = -2(1^2) + 4(1) - 4
-4 = -2 + 4 - 4
-4 = -2
This equation is satisfied by the third point, so it is part of the parabola.

Therefore, the equation, in standard form, of a parabola that contains the given points is:
y = -2x^2 + 4x - 4