How would I identify the vertex and the y intercept of the graph of each funtion?

Question

example: y=3(x-2)squared - 4

Answer 1

3(x^2-4x-4)-4
3x^2-12x-12-4
y =3x^2-12x-16
for the vertes use x=-b/2a
x=12/2(3)=2
3(2)^2-12(2)-16=3*4-24-16=12-24-16=-12-16=-28
vertex is (2,-28)
for the y intercept x = 0
3(0)^2-12(0)-16 = -16
y intercept = -16 or (0,-16)

Answer 2

The y intercept is the value of the function when x = 0, so in the example y = 3(-2)^2-4 =8
If by vertex you mean the local maxima and/or minima, then you need to take the derivative of the functions and solve it e.g dy/dx = 0.. in the example
y = 3(x^2-4x+4)-4
dy/dx=6x-12 = 0
then its vertex should be
6x-12 = 0
6x = 12
x = 12/6 = 2
substituting the obtained value into the original function
y = 3(2-2)^2-4 = -4
the vertex is at (2,-4)

Answer 3

This is a parabolic equation. the vertex will be at the base of the function, or in this case, where (x-2)=0. So we know the x-coefficient will be at 2. With that out of the way, solve for y, and you get -4. So the vertex is at (2,-4).

The y-intercept will be where x=0. Simply plug in 0 for x and solve for y. you get y=3*(-2)^2-4, which is 3*4, or 12, -4, which is 8. So the y-intercept is at (0,8). E-mail me if you have more questions.

Answer 4

All of the answers are in the form of "slope y intercept form" so you are in luck. Slope y intercept form is the following form of a line: y=mx+b where m = the slope of the line and b = the y intercept of the line. It's pretty easy to understand the y intercept part, because the y intercept is when x = 0. So when x= 0, y=b. So for question one, y=-x. You could also write this as y=-1x+0 which is similar to y=mx+b. in this case: m=-1 and b=0. The slope is -1 and the y intercept is 0. 2. m=2 b=1 3. m=1 b =-4 4. m=-3 b=3

Answer 5

y = 3(x-2)^2 - 4
If the equation is in the form y-k = p(x-h)^2, then the vertex is at (h,k).
y+4 =3(x-2)^2 shows the vertex is at (2,-4).
The y-intercept is obtained by setting x=0, so
y-intercept = 3(0-2)^2 -4 = 3*4 -4 = 8

You said each function, but I don't see any more.

Answer 6

Generally speaking you are to use the differentiation. y = f(x) ==> y' = f' (x). Then f' (x) = 0. by solving this equation and inserting its roots in y = f(x) you can calculate the due values of y-axis of the vertex point.
example: y=3(x-2)squared - 4 = 3*(x-2)^2 - 4 ===> y' = 3*2*(x-2); y' = 0 >>> x-2 = 0>>> x = 2.
y(x=2) = -4 >>> S (+2; -4). Is it clear-cut?

Answer 7

Well the easy way is to take your Casio Graphing Calculator and graph it like you would a line. It will show you the y intercept and the vertex. I'm not sure if i'm right but i think the -4 is the y intercept.

Answer 8

Y intercept = 8
Vertex = (2,-4)