which equation is ( y = 2x^{2}-8x + 9 ) rewritten in vertex form?\n( y = 2(x - 2)^{2}+9 )\n( y = 2(x…

which equation is ( y = 2x^{2}-8x + 9 ) rewritten in vertex form?\n( y = 2(x - 2)^{2}+9 )\n( y = 2(x - 2)^{2}+5 )\n( y = 2(x - 2)^{2}+1 )\n( y = 2(x - 2)^{2}+17 )

which equation is ( y = 2x^{2}-8x + 9 ) rewritten in vertex form?\n( y = 2(x - 2)^{2}+9 )\n( y = 2(x - 2)^{2}+5 )\n( y = 2(x - 2)^{2}+1 )\n( y = 2(x - 2)^{2}+17 )

Answer

Explanation:

Step1: Factor out the coefficient of (x^{2})

Given (y = 2x^{2}-8x + 9), factor out (2) from the first two terms: (y=2(x^{2}-4x)+9)

Step2: Complete the square inside the parentheses

For the quadratic (x^{2}-4x), we use the formula ((a - b)^2=a^{2}-2ab + b^{2}). Here (a=x) and (2ab = 4x), so (b = 2). (x^{2}-4x=(x - 2)^{2}-4) Substitute back into the equation: (y=2((x - 2)^{2}-4)+9)

Step3: Simplify the equation

Expand (2((x - 2)^{2}-4)): (y=2(x - 2)^{2}-8 + 9) (y=2(x - 2)^{2}+1)

Answer:

(y = 2(x - 2)^{2}+1) (the third option)