How Do You Find the X-Intercepts of a Quadratic Function?

[math4life]

Homework Statement

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

Homework Equations

The Attempt at a Solution

My factoring(please 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.

 

[statdad]

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.

 

[math4life]

Got it, thanks! :) Answer my next thread please- lol.