Textbook Question
In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-4) The graph passes through the point (1,4).
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4. Polynomial Functions
Quadratic Functions
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Graph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing.
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Verified step by step guidance1
Identify the standard form of the quadratic function: f(x) = a(x-h)^2 + k, where (h, k) is the vertex.
For the given function f(x) = -(x-5)^2 + 1, identify the vertex (h, k) as (5, 1).
Determine the axis of symmetry, which is the vertical line x = h. Here, it is x = 5.
Find the y-intercept by setting x = 0 in the function: f(0) = -(0-5)^2 + 1.
Determine the intervals of increase and decrease. Since the parabola opens downwards (a < 0), it decreases on (-∞, 5) and increases on (5, ∞).
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