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3 years ago

Write y = x2 - 4x + 6 in vertex form.

Mathematics

2 answers:

Anuta_ua [19.1K]3 years ago

6 0

Answer:

y = (x-2)² + 2

Step-by-step explanation:

Converting y = x² - 4x + 6 in vertex form simply means converting from standard form y = ax² - bx + c to the vertex form y = a(x-h)² + k

To start always check and make sure your a=1

In this equation our a=1

Next is to find (b/2)²

(b/2)² = (-4/2)² = (-2)² = 4

Now we want to create a perfect square in our given equation, to do that we will add the value of (b/2)² which is equal to 4 to the linear and quadratic term. That is;

y = x² - 4x + 6

y =( x² - 4x + 4) + 6

Since we added 4 into the parenthesis, we will subtract 4 outside the parenthesis to normalize the equation

y = (x² - 4x + 4) + 6 -4

We now have y = (x² - 4x + 4) + 2 ---------(1)

In the parenthesis we have: x² - 4x + 4 and this is a perfect square, think of the square that will give you this result, and that square is (x-2)²

We will now replace x² - 4x + 4 by (x-2)² in equation (1)

y = (x-2)² + 2

Therefore y = x2 - 4x + 6 in vertex form is y = (x-2)² + 2

pishuonlain [190]3 years ago

3 0

Answer:

(x+2)^2 + 2

Step-by-step explanation:

f (x) = a(x - h)2 + k <--- Vertex Form Equation

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