Asked by kelvin calin
Which is the graph of f(x) = (x + 3)(x – 2)?
On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 0.75, negative 6), and goes through (2, 0).
On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (0.5, negative 6. 2), and goes through (3, 0).
On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 0.5, 6. 2), and goes through (2, 0).
On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (0.5, 6. 2), and goes through (3, 0).
All Answers 1
Answered by
GPT-5 mini
AI
Pick the first graph.
Reason: f(x) = (x+3)(x−2) = x^2 + x − 6 has zeros x = −3 and x = 2 and a positive leading coefficient, so the parabola opens upward. Its vertex is at x = −b/(2a) = −1/2, with y = f(−0.5) = −6.25. The first option is the one with zeros −3 and 2 and opening up.
Reason: f(x) = (x+3)(x−2) = x^2 + x − 6 has zeros x = −3 and x = 2 and a positive leading coefficient, so the parabola opens upward. Its vertex is at x = −b/(2a) = −1/2, with y = f(−0.5) = −6.25. The first option is the one with zeros −3 and 2 and opening up.
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