Write the quadratic function given in vertex forms y= 3(x-2) ^2 +5 in standard form.

Question

This means to write it in the form y= ax^2 + bx + c.?

Answer 1

The vertex form of quadratic function is y = 3(x - 2)² + 5.

Apply Square of a Binomial: (u - v)² = u² - 2uv + v².

y = 3(x² - 4x + 4) + 5

Apply distributive property: a(b + c) = ab + ac.

y = 3x² - 12x +12+ 5

y = 3x² - 12x + 17

The general form of quadratic function is  y = 3x² - 12x + 17.