3. By rewriting $$ f $$ in the form $$ f(x)=a(x-h)^{2}+k $$, sketch the graph and find the domain and range of each of the following functions (a) $$ f(x)=x^{2}-3 x-2 $$ (b) $$ f(x)=2 x^{2}-8 x+7 $$ (c) $$ f(x)=x^{2}-x-6 $$

Question

Burns Campos · Accepted Answer

For $$ f(x)=x^{2}-3x-2 $$, the vertex is at $$(3/2, -17/4)$$, and the domain is all real numbers with a range of $$[-17/4, \infty)$$. For $$ f(x)=2x^{2}-8x+7 $$, the vertex is at $$(2, -1)$$, and the domain is all real numbers with a range of $$[-1, \infty)$$. For $$ f(x)=x^{2}-x-6 $$, the vertex is at $$(1/2, -25/4)$$, and the domain is all real numbers with a range of $$[-25/4, \infty)$$.

3. By rewriting \( f \) in the form \( f(x)=a(x-h)^{2}+k \), sketch the graph and find the domain and range of each of the following functions (a) \( f(x)=x^{2}-3 x-2 \) (b) \( f(x)=2 x^{2}-8 x+7 \) (c) \( f(x)=x^{2}-x-6 \)

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3. By rewriting \( f \) in the form \( f(x)=a(x-h)^{2}+k \), sketch the graph and find the domain and range of each of the following functions (a) \( f(x)=x^{2}-3 x-2 \) (b) \( f(x)=2 x^{2}-8 x+7 \) (c) \( f(x)=x^{2}-x-6 \)

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