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Example: Determining a Quadratic Function from a Graph Using the Vertex (3, -4) and y-intercept (0, 5)
To find a quadratic function from its graph, identify the vertex and another point to substitute into the vertex form, . For example, consider an upward-facing parabola with a vertex at and a -intercept at (0, 5). The vertex (h, k) provides and , yielding the partial equation . To find the coefficient , substitute the coordinates of the -intercept (0, 5) for and : . Solving this equation gives , which simplifies to , so . Therefore, the specific quadratic function for this graph is .
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Intermediate Algebra @ OpenStax
Ch.9 Quadratic Equations and Functions - Intermediate Algebra @ OpenStax
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Example: Determining a Quadratic Function from a Graph Using the Vertex (3, -4) and y-intercept (0, 5)
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A graphic designer is creating a company logo that features a parabolic arch. The designer has identified the vertex of the arch at (2, 8) on a coordinate grid and has correctly substituted these values into the vertex form to obtain the partial equation .
To complete the quadratic function by finding the value of the coefficient , which of the following is the next required step in the standard procedure?
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