4
QuizMultiple Choice

Writing Two-Variable Quadratic Inequalities — Quiz

Question 4 • Advanced Algebra: Concepts and Connections

The parabolic path of a launched projectile contains the vertex open paren 5 comma 120 close paren and the point open paren 25 comma 80 close paren on the boundary. If all the experiments that followed met or exceeded this path, which quadratic inequality in standard form contains the points in the later experiments?

Answer
A
y is greater than or equal to negative 1 tenth times open paren x plus 5 close paren squared plus 120
B
y is less than or equal to negative 1 tenth times open paren x minus 5 close paren squared plus 120
C
y is greater than or equal to negative 1 tenth times open paren x minus 5 close paren squared plus 120
D
y is less than or equal to negative 1 tenth times open paren x plus 5 close paren squared plus 120

Explanation

A parabola with vertex (5, 120) has the form y = a(x − 5)² + 120. Using the boundary point (25, 80), we get 80 = 400a + 120, so a = −0.1. Since later experiments met or exceeded the path, their points satisfy y ≥ −0.1(x − 5)² + 120, which is choice C.

AI-written and checked against the verified answer.

Previous
Next