Question

Convert Y=0.4(X -3)squared +4 to standard form

Answer 1

Answer:

$Y=0.4X^2-2.4X+7.6$

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:

$Y=0.4X^2-2.4X+7.6$