Question

Could someone help me solve this math problem, please? Thanks!

Answer 1

use vertex form
y=a(x-h)²+k
(h,k) is the vertex
a is some number

so
we see the verttex is at (4,-1)
so
h=4 and k=-1
y=a(x-4)²-1

find a

use a point
(3,0)
x=3 and y=0
0=a(3-4)²-1
0=a(-1)²-1
0=a-1
1=a

so da equation is
y=1(x-4)²-1
expanded we get
y=x²-8x+16-1 or
y=x²-8x+15

so that would be B

Answer 2

We can write the factored form of the equation because we know the roots are 3 and 5.
Therefore the factored form is (x-3)(x-5) Remember it is -3 and -5 because of the Zero Product Property.
From here, we can foil. (x-3)(x-5)=x^2-5x-3x+15
That simplifies to x^2-8x+15, which is choice B