How do you identify the important parts of y = x^2 − 36 to graph it?

2 Answers
Jul 4, 2018

See below:

Explanation:

We know we will be dealing with an upward opening parabola, since the coefficient on the x^2 term is positive.

One thing we can do is factor this expression so we can find its zeroes, or x-intercepts.

You might immediately recognize that we're dealing with a difference of squares of the form

a^2-b^2, which factors as (a+b)(a-b). This allows us to factor our expression as

y=(x+6)(x-6)

Setting both factors equal to zero, we get

x=-6 and x=6. These are points we can plot, but it might help to find our y-intercept. Let's set x equal to zero to get

y=-36, which is our y-intercept. Now, we can graph:

graph{x^2-36 [-80, 80, -40, 40]}

Hope this helps!

The given curve

y=x^2-36

x^2=y+36

The above curve shows an upward parabola X^2=4aY which has

Vertex: (x=0, y+36=0)\equiv (0, -36)

Focus: (x=0, y+36=1/4)\equiv(0, -143/4)

Axis of symmetry: x=0