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Math
Secondary 4-6 (Ages 15-18)
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1
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
2
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
3
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
4
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
5
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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