Matemáticas Grados 10–12

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A quadratic function has the form f(x) = ax² + bx + c. Which condition guarantees that its graph opens downward?

A b < 0

B a > 0

C a < 0

D c < 0

The discriminant of a quadratic equation ax² + bx + c = 0 is b² − 4ac. If the discriminant equals zero, what can be concluded about the equation's solutions?

A There is exactly one real solution (a repeated root)

B The solutions are always non-real complex numbers

C There are two distinct real solutions

D There are no real solutions

A line passes through the points (2, 5) and (6, 13). What is the slope of this line?

A 8

B 4

C 1/2

D 2

Which of the following expressions is a perfect square trinomial?

A x² + 6x + 12

B x² + 6x + 9

C x² + 4x + 8

D x² + 5x + 9

The system of equations y = 2x + 1 and y = 2x − 3 is graphed. What is the geometric interpretation of this system?

A The lines are perpendicular and intersect at the origin

B The lines coincide, so there are infinitely many solutions

C The lines intersect at exactly one point

D The lines are parallel and distinct, so there is no solution

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