Question #1c73a

1 Answer
Akaash P.
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)#.

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