This is a graphing problem and I am trying to find the x-intercepts and the y-intercepts. Please show me the full steps. I really appreciate it thank you.

Step-by-step explanation:

To find the y-intercept, set x=0 and evaluate the function.

  f(0) = -3/(0 -4) = 3/4

The y-intercept is (0, 3/4).

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To find the x-intercept(s), set f(x) = 0 and solve for x.

  0 = -3/(x^2 -4)

  0 = -3 . . . . . . . . . . multiply by (x^2 -4), x ≠ ±2

There are no values of x that will make this true. There are no x-intercepts.

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Additional comments

In general, you find the x-intercepts of a rational function by finding the zeros of the numerator. Here, the numerator is -3, so cannot ever be zero.

I find a graphing calculator to be a useful tool for showing where to look for x-and y-intercepts. The attached graph shows y=0 (the x-axis) is a horizontal asymptote, so there are no x-intercepts.

x=2 & x=1

step-by-step explanation:

7*1=7

7*2=14

7 is less than 21

14 is less than 21

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1