Mathematics: Convert y=0.4(x -3)squared +4 to standard form

Convert y=0.4(x -3)squared +4 to standard form

mel2001love

12.01.2022

Y=0.4X^2-2.4X+7.6

Step-by-step explanation:

Given:

The quadratic equation in vertex form is given as:

Y=0.4(X-3)^2+4

The standard form of a quadratic equation is:

y=ax^2+bx+c

Now, in order to convert the given equation into standard form, we have to expand (X-3)^2 using the binomial expansion given by:

(a-b)^2=a^2+b^2-2ab

Here, $a=X\ and\ b= 3$

Therefore,

$(X-3)^2=X^2+3^2-2(X)(3)\\(X-3)^2=X^2+9-6X$

Now, plug in this expanded form into the original equation. This gives,

Y=0.4(X^2+9-6X)+4

Now, we use distribute 0.4 inside the parenthesis. This gives,

$Y=0.4X^2+(0.4\times9)-(6X\times0.4)+4\\Y=0.4X^2+3.6-2.4X+4\\Y=0.4X^2-2.4X+4+3.6\\Y=0.4X^2-2.4X+7.6$

Therefore, the standard form of the given equation is:

Y=0.4X^2-2.4X+7.6

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