Mathematics: Which equation is y = 2x2 – 8x + 9 rewritten in vertex form? y = 2(x – 2)2 + 9 y = 2(x – 2)2 + 5 y = 2(x – 2)2 + 1 y = 2(x – 2)2 + 17

Question 1: 21Question 2: 6Question 3: -3Question 4: 9...

Which equation is y = 2x2 – 8x + 9 rewritten in vertex

emocow

26.07.2020

Option (c) is correct.

The vertex form of the given equation y=2x^2-8x+9 is y=2(x-2)^2+1

Step-by-step explanation:

Given equation y=2x^2-8x+9

We have to rewrite the given equation in vertex form

The general equation in vertex form is y=a(x-h)^2+k , where (h,k) is the vertex.

Consider the given equation y=2x^2-8x+9 ,

taking 2 common from right side, we have

$y=2(x^2-4x+\frac{9}{2})$

Using algebraic identity (a-b)^2=a^2-2ab+b^2

In given equation a = x .....(1)

and -4x = 2ab

using (1) ⇒ -4 = 2b ⇒ b= -2

To make perfect square add and subtract b² = 4 term in equation , we have,

$y=2(x^2-4x+4-4+\frac{9}{2})$

Solving , we have,

$y=2((x-2)^2-4+\frac{9}{2})$

Solving constant term , we have

$y=2((x-2)^2+\frac{-8+9}{2})$

$y=2((x-2)^2+\frac{1}{2})$

Solving , we get,

y=2(x-2)^2+1

Thus, the vertex form of the given equation y=2x^2-8x+9 is y=2(x-2)^2+1

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