Quadratic Functions: Factored Form — Quiz

Question 6 • Algebra I

Which is the graph of f of x is equal to negative open paren x plus 3 close paren times open paren x plus 1 close paren ?

Answer

Image with description On a coordinate plane, a parabola opens up. It goes through 0 comma 3, has a vertex at 2 comma negative 1, and goes through 4 comma 3.

Image with description On a coordinate plane, a parabola opens down. It goes through 0 comma negative 3, has a vertex at 2 comma 1, and goes through 4 comma negative 3.

Image with description On a coordinate plane, a parabola opens up. It goes through negative 4 comma 3, has a vertex at negative 2 comma negative 1, and goes through 0 comma 3.

Image with description On a coordinate plane, a parabola opens down. It goes through negative 3 comma 0, has a vertex at negative 2 comma 1, and goes through negative 1 comma 0.

Explanation

The factors show that the zeros are x = −3 and x = −1, so the graph crosses the x-axis at (−3, 0) and (−1, 0). The negative sign means the parabola opens downward. The axis of symmetry is halfway between the zeros, at x = −2, and f(−2) = −(1)(−1) = 1, giving the vertex (−2, 1). These features match choice D.

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