a quadratic function is represented by g(x)= -2(x-5)^2 +17. what is the equation for this function in standard form?

Answer 1

To convert the quadratic function from vertex form to standard form, we need to expand the expression. The original function is given by:

g(x) = -2(x - 5)² + 17

Let's expand (x - 5)² first:

(x - 5)² = (x - 5)(x - 5) = x² - 5x - 5x + 25 = x² - 10x + 25

Now we'll multiply this expansion by -2:

-2(x² - 10x + 25) = -2x² + 20x - 50

Add the 17 at the end:

g(x) = -2x² + 20x - 50 + 17 = -2x² + 20x - 33

So the equivalent equation of the function in standard form is:

g(x) = -2x² + 20x - 33