Question

The function has a y-intercept and two x-intercepts. It has a minimum point at its vertex. Which function below could this be?

A) f(x) = 2x - 7.
B) g(x) = |x| - 7.
C) h(x) = -2x - 7.
D) p(x) = -|x| - 7.

Answer 1

The correct function that has a y-intercept, two x-intercepts, and a minimum point at its vertex is p(x) = -|x| - 7, which is a downward-opening parabola.

Step-by-step explanation:

The student's question is asking which function has a y-intercept and two x-intercepts, and a vertex that is a minimum point. To satisfy these conditions, the function must be a downward-opening parabola. Among the options provided:

• f(x) = 2x - 7 is a linear function with a positive slope, so it's not the correct choice.
• g(x) = |x| - 7 represents a V-shaped graph, which has a minimum point at its vertex, but only one x-intercept, not two.
• h(x) = -2x - 7 is a linear function with a negative slope, thus it has no minimum point and is not a parabola.
• p(x) = -|x| - 7 is the correct choice as it represents a downward-opening V-shaped graph, which has a vertex that is a minimum point, a y-intercept at -7, and two x-intercepts at x=7 and x=-7.