Question

what is the vertex form of y = x^2 - 20x +15

Answer 1

so your equation is y = x² - 20x + 15. what you'll want to do is complete the square, so take half of 20 and square it. 20/2 = 10. 10² = 100. add 100 to both sides. and simplify x²-20x+100+15 to (x²-10)²+15. now subtract 100 from both sides to get y alone. this leaves you with y = (x²-10)-85. that's your vertex form.

Answer 2

Given a function:
y=ax²-bx+c
The vertex is: (-b/2a, f(-b/2a)

In this case:
y=x²-20x+15
-b/2a=20/2=10
f(10)=10²-20(10)+15=100-200+15=-85

Answer: The vertex is (10,-85)

Given a vertex (h,k), the vertex form is :
y=a(x-h)²+k

In this case:
(10,-85)
a=1
 
y=(x-10)²-85

Answer: y=(x-10)²-85