Grade 11 · Algebra 2
The algebra, geometry, and SAT items US students search most. Written in American English for students, parents, and teachers in the United States.
Open a card to see the answer. These are original practice items for US elementary students — not a state test copy.
Answer: x = (−b ± √(b² − 4ac)) / 2a
It solves ax² + bx + c = 0.
Answer: b² − 4ac
It tells how many real roots.
Answer: no real roots
The graph does not cross the x-axis.
Answer: one real root (a repeated root)
The vertex sits on the x-axis.
Answer: x = −b/(2a)
It is a vertical line through the vertex.
Answer: a > 0
a is the coefficient of x².
Answer: multiply two binomials
(x+2)(x+3) = x² + 5x + 6.
Answer: x = 2 and x = 3
Factors as (x−2)(x−3).
Answer: exactly one output to each input
The vertical-line test checks graphs.
Answer: the output when the input is 3
Substitute 3 for x.
Answer: 9
2(4)+1 = 9.
Answer: allowed inputs
Watch for division by zero and even roots of negatives (over the reals).
Answer: outputs that actually occur
For y = x², range is y ≥ 0.
Answer: f(x) + g(x)
Add outputs.
Answer: plug g(x) into f
Inside first.
Answer: the original function
f(f⁻¹(x)) = x.
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