1. ## parabola!

The graph of y=X^2 is reflected in the axis, then strethced vertically by a factor of 2, and then translated 3 untis to the left and 1 unit down. What is the equation of this parabola? write the answer in standard form and general form.

can you give me a push in the right direction? thanks!!!

2. Originally Posted by brandy
The graph of y=X^2 is reflected in the axis, then strethced vertically by a factor of 2, and then translated 3 untis to the left and 1 unit down. What is the equation of this parabola? write the answer in standard form and general form.

can you give me a push in the right direction? thanks!!!
I'm going to assume it's reflected over the x-axis, as reflecting over the y-axis does nothing to $\displaystyle y = x^2$

So:
1) Reflection over x = 0: Sends y --> -y
$\displaystyle y = x^2$ -->$\displaystyle -y = x^2$

$\displaystyle y = -x^2$

2) Stretching vertically by a factor of 2: Sends y --> (1/2)y (Trust me!)
$\displaystyle y = -x^2$ --> $\displaystyle \frac{1}{2}y = -x^2$

$\displaystyle y = -2x^2$

3) Translate 3 units to the left: Sends x --> x+3
$\displaystyle y = -2x^2$ --> $\displaystyle y = -2(x + 3)^2$

4) Translate 1 unit down: Sends y --> y+1
$\displaystyle y = -2(x + 3)^2$ --> $\displaystyle y + 1 = -2(x + 3)^2$

$\displaystyle y = -2(x + 3)^2 - 1$

-Dan