Put the following in the form a(x-h)^2 + k

a) y= 2x^2-20x+41

THEN STATE THE VERTEX FOR:

b) y= -x^2+14x-46

a.) y = 2x²-20x+41
Complete the Square Formula:
ax²+bx+c → a(x+b/2a)²+(c-b²/4a) → a(x+h)²+k

2x²-20x+41, a = 2, b = -20, c = 41
→ (2)[x+(-20)/2(2)]²+[(41)-(-20)²/4(2)]
→ 2[x+(-20)/(4)]²+[41-(400)/(8)]
→ 2(x-5)²+(41-50)
→ 2(x-5)²+(-9)
→ 2(x-5)²-9
Solution: y = 2(x-5)²-9

b.) vertex: (b/2a,c-b²/4a)
y = -x²+14x-46, a = -1, b = 14, c = -46

vertex: [-(14)/2(-1).(-46)-(14)²/4(-1)]
→ [-14/(-2),(-46-(196)/(-4)]
→ (7,-46+49)
→ (7,3)
Solution: vertex - (7,3)