$\"\"$

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Observe the graph:

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The coordinate points are $\"\"$ and $\"\"$ .

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The standard form of quadratic function $\"\"$ , where $\"\"$ .

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To find the quadratic function represented by the graph, we need to find the values of $\"\"$ and $\"\"$ .

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The $\"\"$ –intercept of the graph is the value of $\"\"$ .

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The graph intersects $\"\"$ –axis at $\"\"$ .

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Value of $\"\"$ is $\"\"$ .

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The equation of the axis symmetry is $\"\"$ .

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Equate the $\"\"$ –coordinate of the vertex to $\"\"$ .

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The $\"\"$ –coordinate of the vertex is $\"\"$ .

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So, $\"\"$ .

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$\"\"$ (Multiply each side by $\"\"$ )

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$\"\"$ (Cancel common terms)

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Substitute the coordinates of the vertex in the equation to find $\"\"$ .

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers: $\"\"$ )

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$\"\"$ (Substitute $\"\"$ and $\"\"$ )

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$\"\"$ (Add $\"\"$ to each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Multiply each side by $\"\"$ )

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$\"\"$ (Cancel common terms)

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Find $\"\"$ .

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify)

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Write the quadratic function.

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$\"\"$ (Standard form of quadratic function)

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$\"\"$ (Substitute $\"\"$ , $\"\"$ and $\"\"$ )

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$\"\"$ (Simplify)

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The quadratic function is $\"\"$ . $\"\"$

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The quadratic function is $\"\"$ .