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

Identify each parabola by zeros, vertex, direction, or y‑intercept:

f(x) = −2x^2 + 24x − 64 = −2(x − 4)(x − 8)
- Opens downward (leading coef −2).
- x‑intercepts at x = 4 and x = 8.
- Axis of symmetry x = 6; vertex at (6, 8) (maximum).
- y‑intercept f(0) = −64.

g(x) = 2x^2 + 24x + 72 = 2(x + 6)^2
- Opens upward (leading coef 2).
- Double root at x = −6 (touches x‑axis there).
- Vertex at (−6, 0) (minimum).
- y‑intercept g(0) = 72.

So the graph that opens down and crosses x at 4 and 8 with vertex (6,8) is f; the graph that opens up and just touches the x‑axis at (−6,0) is g.