SOLUTION: 3. The parabola f(x)=x2 is transformed as described. State the equation that would represent each of the following. a) The parabola is compressed by a factor of 0.5 and shifted

Algebra ->  Equations -> SOLUTION: 3. The parabola f(x)=x2 is transformed as described. State the equation that would represent each of the following. a) The parabola is compressed by a factor of 0.5 and shifted       Log On


   

Question 1198797: 3. The parabola f(x)=x2 is transformed as described. State the equation that would represent each of the following.
a) The parabola is compressed by a factor of 0.5 and shifted 3 units right.


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



4. Describe the transformations applied to f(x)=x2 to produce the function f(x)=2(x-5)2+10




5. Convert the following equation into vertex form by completing the square.
f(x) = 2x2+12x-4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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

-f+%28x%29reflect f+%28x%29 over the x-axis
f+%28-x%29 reflect f+%28x%29+over the y-axis
f+%28x%29+%2B+k+shift+f+%28x%29 up k units
f+%28x%29+-+k+shift f+%28x%29 down+k units
f+%28x+%2B+k%29 shift f+%28x%29 left k units
f+%28x+-+k%29 shift f+%28x%29 right k units
k%2Af+%28x%29 multiply y-values by k (k+%3E+1 stretch, 0+%3C+k+%3C+1 shrink vertical)
f+%28kx%29+divide+%7B%7B%7Bx-values by+k (k+%3E+1 shrink, 0+%3C+k+%3C+1 stretch horizontal)


a) The parabola is compressed by a factor of 0.5 and shifted 3+units right.
0+%3C+0.5+%3C+1 shrink or compress vertically)
y=0.5%28x-3%29%5E2


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%28x%2B5%29%5E2%2B2


4. Describe the transformations applied to f%28x%29=x%5E2 to produce the function
f%28x%29=2%28x-5%29%5E2%2B10
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%28x%29+=+2x%5E2%2B12x-4
f%28x%29+=2+%28x%5E2+%2B+6+x%29+-+4
f%28x%29+=2+%28x%5E2+%2B+6+x%2B3%5E2%29-2%2A3%5E2+-+4
f%28x%29+=2+%28x%2B3%29%5E2-18+-+4
f%28x%29+=2+%28x%2B3%29%5E2-22