Question

What is the range of the graph of y = (x - 7)^2 + 2?

y greater than or equal to 7
y less than or equal to 7
y less than or equal to 2
y greater than or equal to 2

Answer 1

y = (x - 7)^2 + 2

\((x-7)^2 \ge 0\) (because squaring turns negative to positive).

Therefore, \(y \ge 2\)

Answer 2

If we have the equation

\[\Large y = a(x - h)^2 + k\]

where a > 0, then the range is \(\Large y \ge k\)


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If we have the equation

\[\Large y = a(x - h)^2 + k\]

where a < 0, then the range is \(\Large y \le k\)

Answer 3

y = (x - 7)^2 + 2

This is vertical, upright parabola with vertex at (7, 2).
In a vertical upright parabola, the vertex is the lowest point.
Therefore, y will always be greater than or equal to the y-coordinate of the vertex.
\(y \ge 2\)