To convert the vertex form of a quadratic function, which is given by f(x) = a(x – h)² + k, into standard form (Ax² + Bx + C), we need to expand the equation.
In this case, we have:
f(x) = 32(x – 1)² + 0
Step 1: Expand (x – 1)².
(x – 1)² = x² – 2x + 1
Step 2: Substitute this back into the function.
f(x) = 32(x² – 2x + 1)
Step 3: Distribute the 32.
f(x) = 32x² – 64x + 32
Now, we have the quadratic function in standard form, which is:
f(x) = 32x² – 64x + 32