Suppose you are using a computer to draw a face on a coordinate plane. The eyes are at (–3, 3) and (3, 3). The tip of the nose is at the origin. To make a smili

Question

Suppose you are using a computer to draw a face on a coordinate plane. The eyes are at (–3, 3) and (3, 3). The tip of the nose is at the origin. To make a smiling mouth, you are going to enter the equation for the graph of a quadratic function, with its appropriate domain.

Post the quadratic function that you would use (in any form) with the domain. Explain how you determined your equation and why you wrote it in the form that you did.

Answer 1

 

THere are many choices.

 

For example, we can put the endpoint of the mouth

at (-3,-3) and (3,-3) and it bellies down at (0,-6), the vertex

 

So
(-3,-3) (3,-3) (0,-6) <--- vertex

Vertex form is:
y = k(x-k)^2 + k with (h,k) = (0, -6)

 

The equation becomes:
y = k x^2 + -6 = kx^2 - 6

For x=-3 or x = 3, x^2 = 9

Plugging these points into the vertex equation:

-3 = k(9) - 6

3 = 9k

k = 1/3

The equation for the mouth of the parabola is:
y = (1/3)x^2 - 6

with
Domain X = [-3,3]