Convert the quadratic y = 2(x−5)^2 − 10 from vertex form to standard form.
To convert the quadratic equation from vertex form to standard form, we expand the equation:
y = 2(x−5)^2 − 10
y = 2(x−5)(x−5) − 10
Using the FOIL method, we can expand the expression:
y = 2(x^2 - 5x - 5x + 25) - 10
y = 2(x^2 - 10x + 25) - 10
Distributing the 2:
y = 2x^2 - 20x + 50 - 10
y = 2x^2 - 20x + 40
So, the quadratic equation in standard form is:
y = 2x^2 - 20x + 40