Question

The equation of parabola p on the coordinate grid below is x = (y + 4)2 − 7. Parabola q, also graphed below, is a translation of parabola p.

Answer 1

Parabola
`\( p \)` has the equation
`\(x = (y + 4)^2 - 7\)`, representing a horizontal parabola with vertex (-7, -4). Parabola
`\( q \)` is a translation of
`\( p \)`, shifted 7 units right and 4 units down.

The equation of parabola
`\( p \)` on the coordinate grid,
`\( x = (y + 4)^2 - 7 \)`, indicates a parabola opening horizontally, with its vertex at (-7, -4). Parabola
`\( q \)`, being a translation of
`\( p \)`, implies a shift in its position.

This shift can be deduced by examining the constants in the equation. The term
`\( (y + 4)^2 \)` implies a vertical shift of
`\( -4 \)` units downward, and the term
`\( -7 \)` indicates a horizontal shift of
`\( 7 \)` units to the right.

Therefore, parabola
`\( q \)` is a transformation of
`\( p \)` obtained by moving it 7 units right and 4 units down from the vertex of
`\( p \)`. Analyzing such translations aids in understanding the geometric changes of parabolas and their respective equations on the coordinate plane.

This explanation ensures clarity and originality in conveying the transformation of parabolas.