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Write the following expressions in the form
a(x-k)^(2)+h :
a) (i)
x^(2)-6x+4

Write the following expression in the form $a(x-k)^{2}+h$ : $\newline$ $x^{2}-6 x+4$

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Transformations of quadratic functions

Full solution

Q. Write the following expression in the form

a(x-k)^{2}+h

:

\newline

x^{2}-6 x+4

Identify General Form: Identify the general form of the expression we need to achieve, which is $a(x - k)^2 + h$ . $\newline$ Here, $a$ , $h$ , and $k$ are constants.
Complete the Square: Start by completing the square for the expression $x^2 - 6x + 4$ . $\newline$ First, factor out any coefficients from the $x^2$ and $x$ terms if necessary. $\newline$ In this case, the coefficient of $x^2$ is $1$ , so no factoring out is needed.
Focus on $x$ Terms: Focus on the $x$ terms in the expression. $\newline$ The coefficient of $x$ is $-6$ . $\newline$ To complete the square, take half of $-6$ , which is $-3$ , and then square it to get $9$ .
Add and Subtract: Add and subtract $9$ inside the expression to maintain equality. The expression becomes $x^2 - 6x + 9 - 9 + 4$ .
Group Perfect Square: Rewrite the expression by grouping the perfect square trinomial and the constants: $\newline$ $(x^2 - 6x + 9) - 9 + 4$ $\newline$ Simplify the constants to get $(x - 3)^2 - 5$ .
Expression in Desired Form: Now, we have the expression in the desired form: $a(x - k)^2 + h$ , where $a = 1$ , $k = 3$ , and $h = -5$ .

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