Graphs - SAT Math
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Question
What is the equation of a circle with center $(h, k)$ and radius $r$?
What is the equation of a circle with center $(h, k)$ and radius $r$?
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Answer
$(x - h)^2 + (y - k)^2 = r^2$. Standard circle equation with center $(h, k)$ and radius $r$.
$(x - h)^2 + (y - k)^2 = r^2$. Standard circle equation with center $(h, k)$ and radius $r$.
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Question
Which point lies on the line $y = 2x + 3$: (1, 5) or (2, 4)?
Which point lies on the line $y = 2x + 3$: (1, 5) or (2, 4)?
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Answer
(1, 5). Substituting: $y = 2(1) + 3 = 5$, so point $(1, 5)$ satisfies the equation.
(1, 5). Substituting: $y = 2(1) + 3 = 5$, so point $(1, 5)$ satisfies the equation.
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Question
What is the slope-intercept form of a linear equation?
What is the slope-intercept form of a linear equation?
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Answer
$y = mx + b$. Standard form where $m$ is slope and $b$ is y-intercept.
$y = mx + b$. Standard form where $m$ is slope and $b$ is y-intercept.
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Question
Identify the vertex of the parabola $y = (x - 3)^2 + 2$.
Identify the vertex of the parabola $y = (x - 3)^2 + 2$.
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Answer
(3, 2). Vertex form $(x - h)^2 + k$ has vertex at $(h, k)$.
(3, 2). Vertex form $(x - h)^2 + k$ has vertex at $(h, k)$.
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