Question

Match each quadratic function to its graph.
f(x)=
–
x2–6x–9=
–
(x+3)2
g(x)=
–
2x2+20x–48=
–
2(x–4)(x–6)

Answer 1

Compute key features and match by those:

f(x) = -(x+3)^2
- Vertex at (-3, 0) (maximum = 0).
- Single (double) x-intercept at x = -3 — parabola is tangent to the x-axis there.
- y-intercept f(0) = -9.
So pick the graph that touches the x-axis at (-3,0) and opens downward, passing through (0, -9).

g(x) = -2(x-4)(x-6)
- Roots at x = 4 and x = 6.
- Axis of symmetry x = 5, vertex at (5, 2) (maximum = 2).
- y-intercept g(0) = -48.
So pick the graph that crosses the x-axis at 4 and 6, has its peak at (5,2), and opens downward (narrower than y = -x^2).

If you paste or label the graphs, I’ll indicate which label corresponds to f and which to g.