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Quadratic thing

I got the answer but i need like a step by step explanation because i dont get it :/

Quadratic thing I got the answer but i need like a step by step explanation because-example-1
User McNab
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1 Answer

6 votes

Answer:

(0, -2) and (3, 1)

Explanation:

y = x - 2, y = (x - 1)² - 3

To solve this problem, we need to find when the x and ys in both equations are equal.

So,

y = x - 2 = y = (x - 1)² - 3

x - 2 = (x - 1)² - 3

Simplify right side.

x - 2 = x² - 2x - 2

Subtract both sides by (x² - 2x - 2)

x - 2 - (x² - 2x - 2) = 0

Simplify.

-x² + 3x = 0

Factor x.

x (-x + 3) = 0

Because the only way to get a product of 0 is to multiply a number by 0, either x = 0 or (-x + 3) = 0 (x would be 3 in this equation)

So, x = 0 or x = 3

Now, to find y, plug x = 0 x = 3 into one of the equations.

When x = 3, y = x - 2 = 3 - 2 = 1

When x = 0, y = x - 2 = 0 - 2 = -2

Just in case, let's check these values.

Put x = 0 and y = -2 into y = (x - 1)² - 3

-2 = (0 - 1)² - 3 = (-1)² - 3 = 1 - 3 = -2

So, x = 0 and y = -2 is correct.

Put x = 3 and y = 1 into y = (x - 1)² - 3

1 = (3 - 1)² - 3 = 2² - 3 = 4 - 3 = 1

So, x = 3, y = 1 is correct.

Thus, the answers are

(0, -2) and (3, 1)

I hope this helps! Feel free to ask any questions!

User Martin Meeser
by
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