Question

Use what you've learned to write the equation of a parabola that is narrower than y = x ,

2
opens downward, and has vertex (2, – 4).

Answer 1

y = -a(x – 2)² – 4

a > 1

Example:

y = -2(x – 2)² – 4

Explanation:

y = a(x – h)² + k

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vetex: (h, k)

a: vertical reflection or stretch/compression

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If it opens downward, has a vertex of (2, -4) and is narrower than y = x².

Then x² will have a negative coefficient of less than -1 and the input of x will be subtracted by the x value of the vertex which is 2, and the output will be added by the y value of the vertex which is -4.

Therefore y = -a(x – 2)² – 4 where a > 1