Sketching A Graph of an Equation

7.16.4 Sketching A Graph of an Equation

7.16.4 • Sketching A Graph of an Equation

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What is the $x$ -coordinate of the vertex of the graph defined by $y = (x - 3)^{2} + 2$ ?

3. The $x$ -coordinate of the vertex is found by using the squared term of the vertex form. The $x$ -coordinate of the vertex of the graph is 3.

What is the $y$ -coordinate of the vertex of the graph defined by $y = (x - 3)^{2} + 2$ ?

2. In vertex form, the $y$ -coordinate of the vertex is the constant. The value of the $y$ -coordinate of the vertex of the graph is 2.

Find the coordinates of two other points on the graph. The points should be symmetric across the vertex. Show your reasoning.

Compare your answer:

$(0, 11)$ and $(6, 11)$ . When $x$ is 0, the value of $y$ is $(- 3)^{2} + 2$ or 11. The other point is 3 units to the right of the vertex with the same $y$ -coordinate.

Use the graphing tool or technology outside the course. Draw a graph that represents the equation $y = (x - 3)^{2} + 2$ .

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Compare your answer:

Graph of a parabola on a coordinate plane. The x-axis has a scale of 1 extending from negative 12 to 12. The vertical-axis extends from negative 24 to 24 with a scale of 2. Three points on the parabola are labeled: (0, 11), (3, 2), and (6, 11).