Question

Match each quadratic function to its graph.
f(x)=
–
2x2–20x–42=
–
2(x+7)(x+3)
g(x)=x2–18x+81=(x–9)2

Answer 1

Find key features:

f(x) = -2x^2 - 20x - 42 = -2(x+7)(x+3)
- Opens downward (leading coeff. -2).
- x-intercepts at x = -7 and x = -3.
- Vertex at midpoint x = (-7 + -3)/2 = -5; f(-5) = 8 → vertex (-5, 8).
- y-intercept f(0) = -42.

g(x) = x^2 - 18x + 81 = (x-9)^2
- Opens upward.
- Double root at x = 9 (tangent to the x-axis at (9,0)).
- Vertex at (9, 0).
- y-intercept g(0) = 81.

So: the graph that opens downward and crosses the x-axis at -7 and -3 (vertex at (-5,8)) is f. The graph that opens upward and just touches the x-axis at (9,0) is g.