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$\"\"$ The equation is $\"\"$

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$\"\"$

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Quadratic function represents parabola in the graph.

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Compared to the quadratic function $\"\"$

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$\"\"$

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since $\"\"$ then the parabola open upwards.

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Vertex is $\"\"$

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Axis of symmetry $\"\"$

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$\"\"$

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$\"\"$

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Axis of symmetry is $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Vertex is $\"\"$

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Find the $\"\"$ - intercepts by substituting $\"\"$ in $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Since discriminant $\"\"$ , then the roots are imaginary.

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There is no $\"\"$ -intercepts.

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Find the $\"\"$ - intercept by substituting $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Graph:

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Draw the coordinate plane.

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Plot the axis of symmetry, vertex and $\"\"$ -intercepts.

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Connect the plotted points with a smooth curve.

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$\"\"$ Domain of the quadratic function is all real numbers.

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Domain set of $\"\"$ is $\"\"$ .

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Domain in interval notation $\"\"$

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Range set of $\"\"$ is $\"\"$ .

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Range in interval notation $\"\"$ .

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$\"\"$ Observe the graph $\"\"$ increasing on $\"\"$ and decreasing on $\"\"$ .

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Resultants of $\"\"$ are shown in the figure below.

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$\"\"$ Domain in interval notation $\"\"$ and range in interval notation $\"\"$ .

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$\"\"$ $\"\"$ increasing on $\"\"$ and decreasing on $\"\"$ .