Question 1198797

 3. The parabola f(x)=x2 is transformed as described. State the equation that would represent each of the following.


{{{-f (x)}}}reflect {{{f (x)}}} over the {{{x}}}-axis
{{{f (-x)}}} reflect {{{f (x) }}}over the {{{y}}}-axis
{{{f (x) + k }}}shift{{{ f (x)}}} up {{{k}}} units
{{{f (x) - k }}}shift {{{f (x)}}} down{{{ k}}} units
{{{f (x + k)}}} shift {{{f (x)}}} left {{{k}}} units
{{{f (x - k)}}} shift {{{f (x)}}} right {{{k}}} units
{{{k*f (x)}}} multiply {{{y}}}-values by {{{k}}}   ({{{k > 1}}} stretch, {{{0 < k < 1}}} shrink vertical)
{{{f (kx) divide {{{x}}}-values by{{{ k}}}   ({{{k > 1}}} shrink, {{{0 < k < 1}}} stretch horizontal)



a) The parabola is compressed by a factor of {{{0.5}}} and shifted {{{3 }}}units right.

{{{0 < 0.5 < 1}}} shrink or compress vertically)

{{{y=0.5(x-3)^2}}}



b) The parabola is stretched by a factor of {{{2}}}, reflected about the {{{x}}}-axis, shifted {{{5}}} units left and {{{2}}} units up.

{{{y=-2(x+5)^2+2}}}



4. Describe the transformations applied to {{{f(x)=x^2}}} to produce the function 

{{{f(x)=2(x-5)^2+10}}}

the parabola is stretched by a factor of {{{2}}},shifted {{{5 }}}units right and {{{10}}} units up



5. Convert the following equation into vertex form by completing the square.

{{{f(x) = 2x^2+12x-4}}}

{{{f(x) =2 (x^2 + 6 x) - 4}}}

{{{f(x) =2 (x^2 + 6 x+3^2)-2*3^2 - 4}}}

{{{f(x) =2 (x+3)^2-18 - 4}}}

{{{f(x) =2 (x+3)^2-22}}}