Question

Write a quadratic equation with the given transformations from the parent function y = x2
4) Reflect over x-axis, shift to the left 5 units, shift up 7 units
5) Vertical stretch by a factor of 4, shift down 11 units
6) Vertical compression by a factor of, reflect over x-axis, shift to the right 2 units, shift up 3 units.

Answer 1

Answer:

4

Step-by-step explanation:

Answer 2

By Using the Transformations of the parabola

$y = -(x+5)^2+7\\y=4x^{2} +7\\y = -(x-2)^2+3$

• Vertical Translation  move the graph vertically - up or down

$y = x^2+ k$

• Horizontal Translation move the graph horizontally - left or right

$y = (x - h)^2$

Reflection in x-axis  

• flip the graph over the x-axis, (negates the y-values of the coordinates)

$y = -(x^2)$

Reflection in y-axis

• flip the graph over the y-axis,(negates the x-values of the coordinates)

$y = (-x)^2$

• Stretch or Compress Vertically  

stretches away from the x-axis or compresses toward the x-axis

$y = a .x^2$

| a | > 1 is a stretch;

0 < | a | <1 is a compression

• Stretch or Compress Horizontally

stretches away from the y-axis or compresses toward the y-axis

$y=\frac{1}{a} x^{2}$

| a | > 1 is a compression by factor of 1/a;

0 < | a | <1 is a stretch by factor of 1/a

Now, we have $y=x^2$

4). Reflect over x-axis, shift to the left 5 units, shift up 7 units

$y = -(x+5)^2+7$

5) Vertical stretch by a factor of 4, shift down 11 units

$y=4 x^{2} +7$

6) Vertical compression by a factor of, reflect over x-axis, shift to the right 2 units, shift up 3 units.

$y=-(x-2)^{2} +3$

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