Question

Match each quadratic function to its graph.
f(x)=
–
2x2+32x–126=
–
2(x–7)(x–9)
g(x)=x2+1

Answer 1

I don’t see the graphs you want matched, but here are the distinguishing features so you can match them:

f(x) = −2x^2 + 32x − 126 = −2(x − 7)(x − 9)
- Opens downward (a = −2).
- x-intercepts at x = 7 and x = 9 (two real roots).
- Axis of symmetry x = 8; vertex at (8, 2) (maximum).
- y-intercept f(0) = −126.

g(x) = x^2 + 1
- Opens upward (a = 1).
- No real x-intercepts (minimum is above the x-axis).
- Vertex at (0, 1).
- y-intercept g(0) = 1.

So: whichever graph opens up and has its minimum at (0,1) is g(x). The graph that opens down and crosses the x-axis at 7 and 9 (with a maximum at (8,2)) is f(x). If you upload or label the graphs, I’ll match them explicitly.