Convert the quadratic y = 2(x−5)2 − 10

Question

from vertex form to standard form.(2 points)
The standard form of the quadratic is y=
x2+
x+
.

Answer 1

To convert the quadratic from vertex form to standard form, we start with the given vertex form of the quadratic:

\[ y = 2(x - 5)^2 - 10 \]

Now, we will expand and simplify this expression step by step.

1. First, expand the squared term:

\[ (x - 5)^2 = x^2 - 10x + 25 \]

2. Substitute this back into the equation:

\[ y = 2(x^2 - 10x + 25) - 10 \]

3. Distribute the 2:

\[ y = 2x^2 - 20x + 50 - 10 \]

4. Combine like terms:

\[ y = 2x^2 - 20x + 40 \]

Now, we have the quadratic in standard form \( y = ax^2 + bx + c \), where \( a = 2 \), \( b = -20 \), and \( c = 40 \).

Thus, the standard form of the quadratic is:

\[ y = 2x^2 - 20x + 40 \]