How do you graph y=x22x5?

2 Answers
Feb 21, 2018

SImple answer: with an online graphing calculator

Explanation:

Instead, you can also graph this by finding the roots. This is done by using the quadratic formula, ie b±b24ac2a

The result of this is that the roots are at x=1.449 and x=3.449

The turning point will be at the point where the derivative is equal to zero. For this step, y=x22x5

So dydx=2x2

dydx=2x2=0

2x=2

x=1

Finally, check the corresponding y-coordinate at x=1

y=x22x5

y=1225=17=(6)

And as this is a quadratic, you just fill in the line in the usual x2 shape, making the line fit the points we have found above.

Feb 21, 2018

You can find the Vertex, zeroes, y-intercept, and additional points.

Explanation:

You can find the roots by using the quadratic formula:

b±b24ac2a

Here,

a=1

b=2

c=5

Plug in.

(2)±(2)241521

2±242

Simplify:

2±642

2±262

1±6

The y-int of the equation ax2+bx+c is c.

The y-int here is 5.

To find the vertex, turn to vertex form by completing the square:

y=a(xh)+k with (h,k) as the vertex:

(x22x+(1)2(1)2)5

(x1)26

The vertex is (1,6)

Here is a graph for reference: graph{x^2-2x-5 [-9, 11, -6.6, 3.4]}