Question

The vertex form of the equation of a parabola is y=1/2(x-4) squared+13. What is the standard form of the equation?

Answer 1

Given:

$y = \frac{1}{2} {(x - 4)}^{2} + 13$

simplify the square factor:

$y = \frac{1}{2} ( {x}^{2} - 8x + 16) + 13$

$y = \frac{1}{2} {x}^{2} - 4x + 8 + 13$

the solution is then:

$y = \frac{1}{2} {x}^{2} - 4x + 21$