Question

Work each matching problem.Match each equation in Column I with a description of its graph from Column II as it relates to the graph of y = x².I IIa. y = (x - 7)² A. a translation to the left 7 unitsb. y = x² - 7 B. a translation to the right 7 unitsc. y = 7x² C. a translation up 7 unitsd. y = (x + 7)² D. a translation down 7 unitse. y = x² + 7 E. a vertical stretching by a factor of 7

Accepted Answer

Identify the base graph: The parent function is $$y = x$$^{2}$$, which is a parabola centered at the origin. Understand horizontal translations: For equations of the form y = (x$$ - $$h)^{2}$$, the graph shifts horizontally. If $$h is $$positive, the graph moves right by $$h$$ units; if $$h is $$negative, it moves left by $$|h|$$ units. Understand vertical translations: For equations of the form $$y = x$$^{2}$$ + k$$, the graph shifts vertically. If $$k is $$positive, the graph moves up by $$k$$ units; if $$k is $$negative, it moves down by $$|k|$$ units. Understand vertical stretching: For equations of the form $$y = a x$$^{2}$$, where a$$ \u003e 1$$, the graph is vertically stretched by a factor of a$, making it narrower. Match each equation to its description by applying these rules: (a) y = (x$$ - $$7)^{2}$$ shifts right 7 units, (b) $$y = x$$^{2}$$ - 7$$ shifts down 7 units, (c) $$y = 7 x$$^{2}$$ is a vertical stretch by factor 7, (d) y = (x$$ + $$7)^{2}$$ shifts left 7 units, and (e) $$y = x$$^{2}$$ + 7$$ shifts up 7 units.

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Key Concepts

Horizontal Translations of Quadratic Functions

Vertical Translations of Quadratic Functions

Vertical Stretching of Quadratic Functions