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 plotted points

Using the Quadratic Parent Function knowledge point

• The plotted points form a symmetric, U-shaped curve that opens upward.
• The vertex of this curve is located at the origin \((0,0)\).
• The shape is symmetric with respect to the y-axis.

Identify the matching function type

Using the Quadratic Parent Function knowledge point

• A U-shaped symmetric curve is characteristic of a parabola, which is modeled by a quadratic function of the form \(y = ax^2\).
• Linear functions form straight lines.
• Exponential functions grow or decay rapidly in one direction without symmetric U-shaped behavior.
• Square root functions start at a point and curve in one direction.
• Therefore, a quadratic function is the correct model.

Answer:

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