Question

Match each quadratic function to its graph.
f(x)=
–
2x2+24x–64=
–
2(x–4)(x–8)
g(x)=2x2+24x+72=2(x+6)2

Answer 1

I can't see the graphs you have, but here are clear features to use to match each function to its graph:

f(x) = −2x^2 + 24x − 64 = −2(x − 4)(x − 8)
- Opens downward (leading coefficient −2).
- x-intercepts (roots): x = 4 and x = 8.
- Axis of symmetry: x = 6.
- Vertex: (6, 8).
- y-intercept: f(0) = −64.
- Narrower than y = x^2 because |a| = 2.

g(x) = 2x^2 + 24x + 72 = 2(x + 6)^2
- Opens upward (leading coefficient 2).
- Double root at x = −6 (touches the x-axis there).
- Vertex (minimum): (−6, 0).
- y-intercept: g(0) = 72.
- Narrower than y = x^2 because a = 2.

Match using these diagnostics:
- The graph that touches the x-axis at x = −6 and has its vertex on the x-axis is g(x).
- The graph that crosses the x-axis at x = 4 and 8 and has a vertex at (6, 8) is f(x).

If you paste or upload the images (or tell me which graph has those features), I’ll label them for you.