Question

The axis of symmetry of a parabola is x=2. The Parabola crosses the x-axis at the point (5.5,0) At what other point does the parabola cross the x-axis

Answer 1

The parabola crosses the vertical line that passes x-axis at the point (-1, 0).

Step-by-step explanation:

The equation of a parabola can be written in the form y = ax + bx², where a and b are coefficients. The axis of symmetry of a parabola is the vertical line that passes through the vertex. In this case, the axis of symmetry is x = 2. Since the parabola crosses the x-axis at the point (5.5,0), we can use this information to find the other point where the parabola crosses the x-axis.

Since the parabola is symmetric with respect to the axis of symmetry, the other x-intercept will have the same distance from the axis of symmetry as the given x-intercept. So, the other x-intercept will be 3 units to the left of the axis of symmetry.

Therefore, the parabola crosses the x-axis at the point (2 - 3, 0), which simplifies to (-1, 0).

Answer 2

(- 1.5, 0 )

Step-by-step explanation:

The axis of symmetry is midway between the x- intercepts , where it crosses the x- axis, then

5.5 - 2 = 3.5 ← distance from x = 2 to (5.5, 0 )

The other x- intercept is to the left of x = 2

2 - 3.5 = - 1.5

The parabola crosses the x- axis at (- 1.5, 0 )