Question

5. What is the equation of g? Write the equation in vertex form and standard form. Let gbe a quadratic function whose graph is a translation 3 units left and 2 units down of the graph of f(x) (= x2

Answer 1

The vertex form is given by:

$\begin{gathered} y=a(x-h)^2+k \\ \end{gathered}$

And the standard form is given by:

$y=ax^2+bx+c$

The parent function is:

$f(x)=x^2$

After a translation 3 units left and 2 units down:

$\begin{gathered} g(x)=(x+3)^2-2\text{ (vertex form)} \\ g(x)=x^2+6x+7\text{ (standard form)} \end{gathered}$

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$\begin{gathered} V(h,k) \\ h=\frac{-b}{2a} \\ k=f(h) \\ for_{\text{ }}V(0,-4) \\ g(x)=(x-0)^2-4=x^2-4 \\ for_{\text{ }}V(2,-2) \\ g(x)=(x-2)^2-2 \end{gathered}$