how do I freakin' graph y=-x^2+4x-4?!?

Question

I hate graphing parabolas, the teacher didnt show me how. I screwed up in Algebra 1 in the school and now in summerschool I am. please show me how in detailed steps and be bery clear... thanks.

(The first X is negative)

Answer 1

Since x^2 is negative the parabola will have a maximum and be shaped like an upsidedown U. The y-intercept is -4. You get this by setting x = 0. The axis of symmetry is x= -b/2a which in this case is x= -4/2(-1) = 2. The vertex lies on the axis symmetry, so find y=f(2) = -(2^2) +4*2 -4 = 0. So the vertex is at (2,0). So the vertex lies on the x-axis.

So draw a vertical line through the point (2,0). This is the axis of symmetry The point (2,0) is also the vertex of the parabola. So start at the vertex and draw a parabola that goes through the y axis at (0,-4) and continues downward. Draw the right side of the parabola so it is symmetric to the left side.

If you need to you can always compute a few points on the parabola by assigning a value to x and see what y turns out to be. For example if x = -1, y= -9, So plot the point (-1,-9) and make sur your parabola goes through it. Use symmetry to help finishing off the graph.

Answer 2

vertex is found by x = -b / 2a and since a=-1, b=4 and c=-4

x = -4 / 2(-1) or 2 then x = 2 so substitute in the original

y = - (2)^2 + 4(2) -4

y = -4 + 8 - 4 or y = 0

vertexex is @ (2,0)

next, the y-intercept is -4 or point (0,-4)

plot the points to see the left branch and draw the mirror image to see the right.

Answer 3

listen it's pretty easy, just substitute the x.
x=0
y=-(0)^2+4(0)-4
y=-4

then x=1
y=-(1)^2+4(1)-4
y=-1

x=2

x=3

x=4

you can also use -1, -2, -3, -4

then you make the graph

y
3 l
2 l
1 l
0 l---------------------------------------x
-1 l
-2 l
-3 l
-4 l
see? now that you've found the y, just find them, for example when x is 1, y is -4, place a dot where they intercept each other, and so on...

Answer 4

y=-x^2+4x-4=-(x-2)^2
vertex: (2,0)
axis of symmetry: x = 2
Once you have the vertex and the axis of symmetry, you only need to add a couple of points in the same side around the vertex to graph one half of the function.
(0, -4)
(1, -1)
...
Then by symmetry, you can graph the other half.

Answer 5

if x =1 then y= - (1)^2 + 4*(1)-4 = -1

caclulate
x= -2, y=-16
x = -1, y= -9
x=0 , y= -4
x=1, y = -1
x= 2, y= 0
x=3, y= -1
x=4, y= -4
etc....

Answer 6

Since there's are so many answers already, I'll just give u a useful website to check your answers.


enter this: -x^2+4x-4

and click "evaluate"

http://www.coolmath.com/graphit/index.html

Good luck with summer school!