Find The Equation Of A Parabola In Vertex Form That Has Been Translated 5 U

Solution

Hello Ye,

The original parabola equation is f(x) =x2

It is translated 5 units left —> g(x) = (x+5)2

It is also translated 11 units up —-> h(x) = (x+5)2 + 11

It passes through (3,27) so make the equation h(x) = a*(x+5)2 + 11, then replace x and h(x) by 3 and 27 respectively to solve for a: 27 = a*(3+5)2 + 11 —-> 27 = a*(8)2 + 11 —> 27 = 64*a + 11

Subtract 11 from both sides: 16 = 64*a

Divide by 64 on both sides: 1/4 =a

So the complete equation in vertex form is h(x) = (1/4)*(x+5)2 + 11

Cheers.