Question

sophia plots points on a graph to represent the shape of a concave lens.

which type of function should sophia use to model the shape of the lens?

• linear
• exponential
• quadratic
• square root

Explanation:

Analyze the shape of the plotted points

Using the Graph Interpretation knowledge point
The plotted points on the coordinate plane form a symmetric, U-shaped curve that opens upward. The minimum value of the curve is located near the origin, and the points rise symmetrically on both the left and right sides of the y-axis.

Identify the matching function type

Using the Quadratic Parent Function knowledge point

$$ y = x^2 $$

• A linear function forms a straight line.
• An exponential function grows or decays rapidly in one direction without symmetric U-shaped behavior.
• A quadratic function forms a parabola, which matches the symmetric U-shape of the plotted points.
• A square root function starts at a specific endpoint and curves gradually in one direction.

Therefore, a quadratic function is the most appropriate model.

Answer:

• linear
• exponential
• quadratic (Correct answer)
• square root