Consider the function \(f(x)=x^2-6x+7\).
\(a\) Find the coordinates of the vertex of the graph of \(f\).
\(b\) Write down the equation of the axis of symmetry of the graph of \(f\).
\(c\) The graph of \(f\) is translated 3 units in the positive \(x\)-direction and 2 units in the negative \(y\)-direction. Find the equation of the translated graph, giving your answer in the form \(y=ax^2+bx+c\).
Question
Find the coordinates of the vertex of \(f(x)=x^2-6x+7\).
Hint
Hint
Hint
Use \(x=-\frac{b}{2a}\) to find \(x\), then substitute back into \(f(x)\) for \(y\).
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Complete Answer
The vertex is \((3,-2)\).
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Question
Write down the equation of the axis of symmetry of \(f(x)\).
Hint
Hint
Hint
Recall that the axis of symmetry is the vertical line passing through the vertex.
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The axis of symmetry is \(x=3\).
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Question
The graph of \(f(x)=x^2-6x+7\) is translated 3 units in the positive \(x\)-direction and 2 units in the negative \(y\)-direction. Find the equation of the translated graph in the form \(y=ax^2+bx+c\).
Hint
Hint
Hint
Translate the vertex to get the new vertex, then write the equation in vertex form and expand it.
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The translated graph has the equation \(y=x^2-12x+32\).
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