how would I graph f(x)=x^2-x-2? I am thinking that this graph would look like a diagonal line.?

Question

how would I graph f(x)=x^2-x-2? I am thinking that this graph would look like a diagonal line.?

Answer 1

It will be a parabola with y-intercept = -2. Since -x is also included, the right side will be slightly lower than the left side (since -x causes an decrease for x > 0 and an increase for x < 0). This will offset the vertex to the right.



This is a quadratic function so you can find the x-coord of the vertex with the formula x = -b/(2a), then use the f[-b/(2a)] to find the corresponding y-coord.



The vertex will be at (1/2, -9/4).

Answer 2

x^2 always translates to some parabola, as long as there's no x^3, x^4, etc. If it's -x^(2), then it would be an upside down parabola, but it's not, so it will be right side up.



One method would be to complete the square and look at where it's zero along the axis.

Look for two factors of -2 that add up to -1: -2 and 1 work.

So, f(x) = (x - 2)(x + 1). If x = 2 or x = -1, then y = 0.

Plot those points...(2,0) and (-1,0) on your graph.

To find the lowest point, it's going to be in the middle between those points you just plotted. So, find the point on your graph in between those two points on your graph or find the mean, whatever works best for you.



-1 + 2 = 1 and the average divides this by two, so 1/2.

Put that value for x into your equation to find the lowest point...

f(1/2) = (1/2)^2 - (1/2) - 2 = 1/4 - 1/2 - 2 = 1-2+4 / 4 = 3/4

So, the bottom point is (-1/2, -1/4). Plot your point there, and just fill up the rest with a curved line going through those points.

Answer 3

The graph of X^2 - X - 2 will be a U-shape Parabola.



The Y-intercept will be -2. (y-int = when x is zero, so replacing x with zero's and you'll get y=-2)



Here's a table:



X | Y

-------

-3| 10

-2| 4

-1| 0

0 | -2

1 | -2

2 | 0

3 | 4



It's a lot easier to do this with a graphing calculator.

Answer 4

it is a parabola.

x f(x)=x^2-x-2

3 4

2 0

1 -2

0 -2

-1 0

-2 4

Answer 5

the fuction , when graphed, would form a curved parabola