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