Answer:
f(x) = 2(x - 2)^2 - 1
vertex: (2, -1)
Explanation:
f(x) = 2x^2 - 8x + 7
First, we find the vertex.
x = -(-8)/4 = 2
y = 2(2)^2 - 8(2) + 7 = 2(4) - 16 + 7 = 8 - 9 = -1
vertex: (2, -1)
Second, we write f(x) in vertex form.
we know that h and k have to be 2 and -1.
2x^2 - 8x + 7 = a(x - 2)^2 - 1
Since 8 - 1 = 7, we do this:
f(x) = (2x^2 - 8x + 8) - 1
Factor out the 2 and then factor the polynomial
f(x) = 2(x^2 - 4x + 4) - 1
factors of 4:
1 4
2 2
-1 -4
-2 -2 = -4
the function in vertex for is:
f(x) = 2(x - 2)^2 - 1