Question

Which equation represents y=x^2-10x+30 in vertex form?

Answer 1

We are given parabola equation y=x^2-10x+30.

We need to convert it in vertex form y= a(x-h)^2+k.

We need to find the value of a, h and k to get the vertex form.

For the given equation y=x^2-10x+30, the coefficient of x^2 is 1.

Therefore, a=1.

Now, let us find values of h and k.

h = -b/2a.

h = -(-10)/2(1) = 5.

Plugging x=5 in given equation to get the value of k.

y= x^2-10x+30 => (5)^2 -10(5) +30 = 25 -50 +30 = 5.

Therefore, k =5.

Therefore, vertex (h,k) = (5,5).

So, the vertex form is

$y=(x-5)^2+5$