`y = (x-3)^2 + 1` Write the quadratic function in standard form.

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violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

Take note that the standard form of a quadratic equation is: `ax^2 + bx + c = 0`
We need to apply the FOIL method for `(x - 3)^2 = (x - 3)(x - 3)` .
First terms: `x* x = x^2 `

Outer terms:` x * - 3 = -3`` x`

Inner terms: `-3 * x = -3x`

Last terms: `-3 * - 3 = 9`

Combining the results for outer terms and inner terms: `-3x + (-3x) = -6x` .
Therefore,` (x - 3)^2 = x^2 - 6x + 9` .

So, we will have: `x^2 -6x + 9 + 1` .

Combining like terms. `x^2 - 6x + 9 + 1 = x^2 - 6x + 10` .

Therefore `y = (x - 3)^2 + 1 ` in standard form is `x^2 - 6x + 10` .

That is it!

jitend786's profile pic

jitend786 | (Level 1) Adjunct Educator

Posted on

` `

Good question!

Standard form implies that you write the highest power (exponent) of x (or the variable in question) first, followed by the next highest power and so on…. For a quadratic equation,  the standard form is written as    `ax^2 +bx+c`

To rewrite `(x-3)^2+1` in this form, expand this expression.

`(x-3)^2+1= (x-3)(x-3) +1`

`= x^2-3x-3x+9+1`

`=x^2-6x+10`

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rupkaur2001's profile pic

rupkaur2001 | Student, Grade 11 | (Level 1) eNoter

Posted on

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

First off, we will use the above expansion in 

`(x-3)^2` So the equation will look like

`y=x^2+9-6x+1` 

`y=x^2 - 6x + 10`

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