Question

which is $y = 2(x - 3)^2 + 10$ in standard form?

a $y = 2x^2 + 10x - 9$

b $y = 2x^2 - 9x + 10$

c none of these

d $y = 2x^2 - 12x + 28$

e $y = 2x^2 - 3x + 10$

Explanation:

Step1: Expand the squared term

We start with the given equation \( y = 2(x - 3)^2+10 \). First, we expand \( (x - 3)^2 \) using the formula \( (a - b)^2=a^{2}-2ab + b^{2} \), where \( a=x \) and \( b = 3 \). So, \( (x - 3)^2=x^{2}-6x + 9 \).

Step2: Multiply by the coefficient

Now, multiply the expanded term by 2: \( 2(x^{2}-6x + 9)=2x^{2}-12x + 18 \).

Step3: Add the constant term

Next, add the 10 from the original equation: \( y=2x^{2}-12x + 18+10 \).

Step4: Simplify the constant terms

Simplify \( 18 + 10=28 \). So, the equation in standard form is \( y = 2x^{2}-12x + 28 \).

Answer:

D. \( y = 2x^{2}-12x + 28 \)