Digital SAT Math Practice Question #1274
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Desmos hack: Type $(x-4)^2 + (y+2)^2 = 25$ and $y = 3$ directly into Desmos. Look at the graph: the circle touches $y = 3$ at exactly one point $(4, 3)$. Instant verification.
The standard equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$. The center is $(h, k) = (4, -2)$, so the equation begins $(x - 4)^2 + (y - (-2))^2 = (x - 4)^2 + (y + 2)^2$. Since the circle is tangent to the horizontal line $y = 3$, the...
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
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The function \( f \) is defined by \( f(x) = c \cdot d^x \), where \( c \) and \( d \) are positive constants. The graph...
>M Note: Figure not drawn to scale. In the \( xy \)-plane, a parabola is given by the equation \( y = x^2 - 6x + 10 \). ...
A radioactive isotope decays such that its mass, \( M(t) \), in grams, after \( t \) days is modeled by the function \( ...
The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 + 6x - 8y - 75 = 0 \] Line \( \ell \) is tangen...