4. Polynomial Functions

Quadratic Functions

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Multiple Choice

Graph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. $f\left(x\right)=-\left(x-5\right)^2+1$

A graphing coordinate with a curve

Verified step by step guidance

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, ∞).

Master Properties of Parabolas with a bite sized video explanation from Patrick

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Expert video explanations

Graph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. f(x)=−(x−5)2+1f\left(x\right)=-\left(x-5\right)^2+1f(x)=−(x−5)2+1