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Question

# Sketch each parabola using the given information. vertex (3,6), y-intercept 2

Solution

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vertex $(3,6)$, $y$-intercept 2

The vertex is on the axis of symmetry at $x=3$

The $y$-intercept at $(0,2)$ is lower than the vertex, so the parabola opens downward.

The $y$-intercept is 3 units to the left of the axis of symmetry at $y=2$. Parabolas are symmetric about the axis of symmetry so there must be a point on the parabola 3 units to the right of the axis of symmetry also at $y=2$. So we have 3 points:

$(3,6)$, $(0,2)$, $(6, 2)$

Plot the three points and draw a downward opening parabola. Make sure that the vertex is the highest point of the graph.

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