91Ó°ÊÓ

Identify the vertex, focus, directrix, and axis of symmetry of the parabola. Describe the transformations of the graph of the standard equation with vertex \((\mathbf{0}, \mathbf{0})\). $$y=\frac{1}{8}(x-3)^2+2$$

Factor the trinomial. $$ 5 x^2+5 x-30 $$

reflection in the \(y\)-axis followed by a translation 4 units right $$ \begin{aligned} h(x) &=f(-x) \\ &=2(-x)^2+6(-x) \\ &=2(x)^2-6 x \\ g(x) &=h(x-4) \\ &=2(x-4)^2+6(x-4) \\ &=2 x^2-10 x+8 \end{aligned} $$

Identify the vertex, focus, directrix, and axis of symmetry of the parabola. Describe the transformations of the graph of the standard equation with vertex \((\mathbf{0}, \mathbf{0})\). $$y=-\frac{1}{4}(x+2)^2+1$$

\(g(x)=-3 x^2-6 x+5\)

\(f(x)=-2 x^2+8 x+7\)

Identify the vertex, focus, directrix, and axis of symmetry of the parabola. Describe the transformations of the graph of the standard equation with vertex \((\mathbf{0}, \mathbf{0})\). $$x=\frac{1}{16}(y-3)^2+1$$

\(g(x)=3 x^2+18 x-5\)

Identify the vertex, focus, directrix, and axis of symmetry of the parabola. Describe the transformations of the graph of the standard equation with vertex \((\mathbf{0}, \mathbf{0})\). $$y=(x+3)^2-5$$

MODELING WITH MATHEMATICS The function f(t) = ?16t2 + 10 models the height (in feet) of an object t seconds after it is dropped from a height of 10 feet on Earth. The same object dropped from the same height on the moon is modeled by g(t) = ? 8 —3 t2 + 10. Describe the transformation of the graph of f to obtain g. From what height must the object be dropped on the moon so it hits the ground at the same time as on Earth?