Question #1c73a

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Question #1c73a

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Answer 1 · 2017-12-18T04:12:15

$y = x^{2} - 5$ $color(blue)(y = x^2 - 5)$

Explanation:

Any quadratic equation can be written in this form:

$y = a x^{2} + b x + c$ $y = ax^2 + bx + c$ .

Since we have 3 $(x, y)$ $(x,y)$ 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:

$- 4 = a + b + c$ $-4 = a + b + c$

$- 4 = a - b + c$ $-4 = a - b + c$

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

$y = a x^{2} + c$ $y = ax^2 + c$ .

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

$- 4 = a + c$ $-4 = a + c$

$- 1 = 4 a + c$ $-1 = 4a + c$

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

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

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Question #1c73a

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