In order to get on the track and field team, Anastacia must be able to find out what is the maximum height she needs to be able to jump. The team provides her with the expression −8x2+80x−191−8x2+80x−191 as one of the examples of height requirements she must complete during the try out. The team explains to her that she must write an equivalent expression to easily show the maximum height required. Her equivalent expression is -8( )² + . Fill in the missing pieces of Anastacia’s expression
Anastacia's equivalent expression is:
-8(x - 5)² + 216
Explanation:
In order to find the missing pieces of the expression, we must first complete the square. The given expression is:
-8x^2 + 80x - 191
To complete the square, we need to factor out the coefficient of x^2, which is -8:
-8(x^2 - 10x) - 191
Next, we need to find the value to complete the square. The value is half the coefficient of x, which is:
-10/2 = -5
Now, we add and subtract (-5)^2 inside the parentheses:
-8(x^2 - 10x + 25 - 25) - 191
-8[(x - 5)^2 - 25] - 191
-8(x - 5)^2 + 200 - 191
-8(x - 5)^2 + 216
Therefore, the missing pieces of Anastacia's equivalent expression are (x - 5)² + 216.