Question

Re-write the quadratic function below in Standard Form
y, equals, 8, left parenthesis, x, minus, 2, right parenthesis, squared, plus, 5
y=
8(x−2)
2
+5

Answer 1

To rewrite the quadratic function \( y = 8(x - 2)^2 + 5 \) in standard form, we need to expand it.

1. Start by expanding the squared term:
\[
(x - 2)^2 = x^2 - 4x + 4
\]

2. Now, substitute this back into the equation:
\[
y = 8(x^2 - 4x + 4) + 5
\]

3. Distribute the 8:
\[
y = 8x^2 - 32x + 32 + 5
\]

4. Combine like terms:
\[
y = 8x^2 - 32x + 37
\]

So, the quadratic function in standard form is:
\[
y = 8x^2 - 32x + 37
\]