Answer:
-8
Step-by-step explanation:
Vertex of function f(x)
From inspection of the graph, the vertex of f(x) is (2, 1)
Vertex of function g(x)
Given: [tex]g(x)=2x^2-8x+1[/tex]
Standard form of a parabola is [tex]y=ax^2+bx+c[/tex]
Vertex form of a parabola is [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex)
To convert from standard to vertex form, complete the square.
Set the equation to zero:
[tex]\implies 2x^2-8x+1=0[/tex]
Add 7 to both sides:
[tex]\implies 2x^2-8x+8=7[/tex]
Factor out common term 2 on left side:
[tex]\implies 2(x^2-4x+4)=7[/tex]
Factor expression inside brackets:
[tex]\implies 2(x-2)^2=7[/tex]
Subtract 7 from both sides:
[tex]\implies 2(x-2)^2-7=0[/tex]
Therefore:
[tex]g(x)=2(x-2)^2-7[/tex]
So the vertex of g(x) is (2, -7)
Solution
y-value of the vertex of f(x) = 1
y-value of the vertex of g(x) = -7
y-value of vertex of f(x) subtracted from the y-value of the vertex of g(x):
-7 - 1 = -8
