Graph each parabola. Give the vertex, axis of symmetry, domain, and range. f(x)=-(2)/(3)(x+2)^2+

step 1 We want to graph and identify the key features for the quadratic function F of x equals negative

Graph each parabola. Give the vertex, axis of symmetry,...

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Key Concepts

Range

The range of a quadratic function is the set of all possible output y-values. Depending on whether the parabola opens upwards or downwards (determined by the sign of a), the range will either be all y-values greater than or equal to the vertex's y-value or less than or equal to it.

Vertex Form of a Parabola

The vertex form of a quadratic function is given by f(x) = a(x-h)² + k, where (h, k) represents the vertex of the parabola. This form makes it easy to identify the vertex and understand the effects of transformations such as translations and vertical stretching or compressing.

Vertex

The vertex of a parabola is the point where the curve reaches its maximum or minimum value. In the context of the vertex form, it is directly given by the coordinates (h, k), and it serves as a key indicator of the graph's overall position in the Cartesian plane.

Axis of Symmetry

The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two mirror-image halves. Its equation is given by x = h, where h is the x-coordinate of the vertex.

Domain

The domain of a quadratic function typically includes all real numbers unless otherwise restricted. This represents all possible x-values that can be input into the function.

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