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Quadratic equation y=(x-5)²-2

2 Answers

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Answer:

x = 3, x = 7

Explanation:

Turn y = (x-5) ²-2 into a quadratic equation

y = x² - 10x + 23

use quadratic formula if needed!

x = (-b +/- (√b²- 4ac)) / 2a

x = (-(-10) +/- (√-10² - 4 (1)(23)) / 2

x = (10 +/- (√100 - 4(23)) / 2

x = (10 +/- (√100 - 92)) / 2

x = (10 +/- (√8)) / 2

x = (10 +/- 2√4) / 2

x = (10 +/- 2(2)) / 2

x = (10 +/- 4) / 2

x = (10 + 4) / 2 x = 14 / 2 x = 7

x = (10 - 4) / 2 x = 6/2 x = 3

User Abhilash Kandwal
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7.9k points
4 votes

The given quadratic equation is y = (x-5)² - 2.

This equation is in vertex form, which is y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Comparing the given equation with the vertex form, we can see that h=5 and k=-2.

Therefore, the vertex of the parabola is (5, -2).

Since the coefficient a is positive, the parabola opens upwards.

To find the x-intercepts, we need to set y = 0 and solve for x:

0 = (x-5)² - 2

Adding 2 to both sides, we get:

2 = (x-5)²

Taking the square root of both sides, we get:

±√2 = x-5

Adding 5 to both sides, we get:

x = 5 ± √2

So the x-intercepts are (5+√2, 0) and (5-√2, 0).

To find the y-intercept, we need to set x = 0:

y = (0-5)² - 2 = 23

So the y-intercept is (0, 23).

We can also plot the vertex and intercepts on a coordinate plane to see the shape of the parabola.

User Adrian Cole
by
7.9k points

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