Question

the graphs of three functions are shown. which statement accurately compares the functions on the graph? all of the functions have a maximum. the square root and quadratic function share a minimum. the absolute value and quadratic function share a y-intercept. the absolute value and square root function share an x-intercept.

Explanation:

1. Analyze "All of the functions have a maximum": The quadratic function (opening up) has a minimum, not a maximum. The square - root function (assuming it's the typical \(y = \sqrt{x + a}\) - like) and absolute - value function (opening down) have different extrema. So this statement is false.
2. Analyze "The square root and quadratic function share a minimum": The square - root function (if it's the one shown, increasing) does not have a minimum in the typical sense (it starts at a point and increases), while the quadratic function has a minimum. So this statement is false.
3. Analyze "The absolute value and quadratic function share a y - intercept": The y - intercept of a function is the value of the function when \(x = 0\). From the graph, the absolute - value function (red) and the quadratic function (blue) both cross the y - axis at the same point (when \(x = 0\), their \(y\) - values are equal).
4. Analyze "The absolute value and square root function share an x - intercept": The x - intercept of the absolute - value function (red) and the square - root function (green) do not appear to be the same from the graph. The square - root function starts at a non - zero \(x\) (or has a different x - intercept) compared to the absolute - value function.

Answer:

The absolute value and quadratic function share a y - intercept.