To determine which statement is true regarding the parabola based on the provided details, we need to clarify the concepts involved:
-
Y-intercept: This is the point where the parabola intersects the y-axis. It occurs when \( x = 0 \).
-
Vertex: This is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.
-
X-intercepts: These are the points where the parabola intersects the x-axis. This occurs when \( y = 0 \).
Now let's analyze the statements:
-
The y-intercept and the vertex share the same point. - This could only be true if the vertex lies on the y-axis and is equal to the y-intercept, which typically is not the case for most parabolas.
-
The vertex and the x-intercepts share the same point. - This would be true only if the vertex is also an x-intercept. This occurs when the vertex is located on the x-axis, but not true for most parabolas unless specifically designed that way.
-
There is only one x-intercept. - This statement can be true for parabolas that are tangent to the x-axis, which means they touch the x-axis at exactly one point.
-
The y-intercept and the x-intercepts share the same point. - This would mean that the y-intercept lies on the x-axis, which is typically not true unless the parabola is particularly special.
Based on general characteristics and without the ability to see the image or its specific details:
- If the parabola has only one x-intercept, this suggests it is tangent to the x-axis, which makes this statement likely the true one among the given options.
Thus, the best conclusion is:
There is only one x-intercept.
1 answer