Question

Which quadratic function is represented by the graph?

y = 5(x – 6)2 + 5
y = 5(x – 7)(x – 5)
y = 5(x + 6)2 – 5
y = 5(x – 7)(x + 5)

Answer 1

I don't see the graph — could you upload it or describe key points (vertex and x-intercepts)?

How to pick quickly:
- Forms 1 and 3 are vertex form: y = 5(x–6)^2+5 has vertex (6,5); y = 5(x+6)^2–5 has vertex (−6,−5).
- Forms 2 and 4 are factored: y = 5(x–7)(x–5) has zeros at x=5 and x=7 (axis x=6) and vertex (6,−5); y = 5(x–7)(x+5) has zeros at x=7 and x=−5 (axis x=1) and a very low vertex at x=1.

So if the graph’s vertex is at (6,−5) or the x-intercepts are 5 and 7, the correct choice is
y = 5(x − 7)(x − 5).

If the vertex is (6,5) pick the first; if (−6,−5) pick the third; if zeros at −5 and 7 (axis x=1) pick the fourth.