How would I write the following quadratic function in standard form?
The function is -(9x+2)^2+4x? What is the process for changing this to standard form?
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To write a quadratic function in standard form, you need to expand and simplify the expression. The standard form of a quadratic function is ax^2 + bx + c, where a, b, and c are constants.
Let's go step by step:
First, let's expand the expression -(9x + 2)^2:
-(9x + 2)(9x + 2)
= -(81x^2 + 4x + 4x + 4)
= -(81x^2 + 8x + 4)
Next, let's distribute the negative sign to each term:
= -81x^2 - 8x - 4
Now, let's add the term 4x:
= -81x^2 - 8x - 4 + 4x
= -81x^2 - 4x - 4
Finally, the expression -(9x+2)^2+4x can be written in standard form as:
-81x^2 - 4x - 4
Therefore, the quadratic function -(9x+2)^2+4x in standard form is -81x^2 - 4x - 4.