# Solving for the X Intercepts

1. Jun 14, 2009

### math4life

1. The problem statement, all variables and given/known data
Sketch the graph of each function given using shifts and stretches of the parent function y=x2 (not by simply plotting points). Clearly indicate and explicitly state the orientation, vertex, axis of symmetry, y-intercept, and point symmetric to the y-intercept, the x-intercepts, and the maximum or minimum value of each function. Use these features to complete your graph.

f(x)=-x2-4x

2. Relevant equations

3. The attempt at a solution
My factoring(plz check):
f(x)=-x2-4x
f(x)=-(x2-4x+4)+4=0
f(x)=-(x-2)2+4=0.
Finding the x intercepts is the part I am stuck on.

The y intercept is obviously 0, so we have 0,0.
I know that the other x intercept will be at 4 due to the similar proportion (I think) but I want to know how to find that.

We get -4=-(x-2)2
+-SQRT(-4)=-x+2
-x=-2+-SQRT(-4)
X=2+-SQRT(-4)

That's a non real answer. Please someone check my math on solving for the x intercept. The rest of the problem I have done.

2. Jun 14, 2009

Here's a hint: look very, very, very, closely, at the signs inside parentheses going from the first row to the second in your work (duplicated below)

\begin{align*} f(x) & = -x^2 - 4x \\ f(x) & = - \left(x^2 - 4x + 4\right) + 4 = 0 \end{align*}

Also, to be mathematically correct, you should hold off on the " = 0 " portion until you've finished re-writing $$f(x)$$
as you want to. After the re-writing, set the new form equal to zero and solve.

3. Jun 14, 2009