Quadratic Functions: Factored Form — Quiz

Question 1 • Algebra I

Which is the graph of f of x is equal to open paren x minus 1 close paren times open paren x plus 4 close paren ?

Answer

Image with description On a coordinate plane, a parabola opens down. It goes through negative 4 comma 0, has a vertex at negative 1 point 7 5 comma 6 point 2, and goes through 1 comma 0.

Image with description On a coordinate plane, a parabola opens up. It goes through negative 4 comma 0, has a vertex at negative 1 point 7 5 comma negative 6 point 2, and goes through 1 comma 0.

Image with description On a coordinate plane, a parabola opens up. It goes through negative 1 comma 0, has a vertex at 1 point 7 5 comma negative 6 point 2, and goes through 4 comma 0.

Image with description On a coordinate plane, a parabola opens down. It goes through negative 1 comma 0, has a vertex at 1 point 7 5 comma 6 point 2, and goes through 4 comma 0.

Explanation

The factors are zero at x = 1 and x = −4, so the graph crosses the x-axis at (1, 0) and (−4, 0). The coefficient of x² is positive, so the parabola opens upward. Its vertex lies halfway between the roots, at x = (1 + (−4))/2 = −1.5; substituting gives f(−1.5) = (−2.5)(2.5) = −6.25. This matches choice B, which opens up and has a vertex near (−1.75, −6.2).

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