Question #1c73a

1 Answer
Dec 18, 2017

color(blue)(y = x^2 - 5)

Explanation:

Any quadratic equation can be written in this form:

y = ax^2 + bx + c.

Since we have 3 (x,y) coordinate points, we are able to solve this three-variable system of equations for a, b, and c. Let's begin!

The first two points are very similar in terms of the resulting equations:

-4 = a + b + c

-4 = a - b + c

If we subtract one equation from the other and simply, we find that b = 0. Now we are just left with

y = ax^2 + c.

Using the second and third (x,y) coordinate points yields

-4 = a + c

-1 = 4a + c

Subtracting one from the other to get rid of the c terms and simplifying will leave us with a = 1. Plugging back into any of the previous equations will give us c = -5 , and we know have all the components for our quadratic equation!

color(blue)(y = x^2 - 5).