Answer:
Option a,d and e are true statements.
Step-by-step explanation:
Given : Function [tex]f(x)=x^2-8x+5[/tex]
To find : Which statements are true about the graph of the function, Check all that apply?
Solution :
The quadratic function is in the form, [tex]y=ax^2+bx+c[/tex]
The vertex form is [tex]y=a(x-h)^2+k[/tex]
To find vertex form we apply completing the square,
[tex]f(x)=x^2-8x+5+4^2-4^2[/tex]
[tex]f(x)=x^2-8x+(4)^2+5-16[/tex]
[tex]f(x)=(x-4)^2-11[/tex]
The vertex form of the function is [tex]f(x)=(x-4)^2-11[/tex]
The 'a' statement is true.
The vertex of the function is (h,k).
On comparing with vertex form, h=4 and k=11
Vertex of the function is (4,11)
The 'b' statement is not true.
The x-coordinate of the vertex i.e. [tex]x=-\frac{b}{2a}[/tex] is the axis of symmetry,
So, [tex]x=-\frac{-8}{2(1)}[/tex]
[tex]x=4[/tex]
The axis of symmetry is x=4.
The 'c' statement is not true.
The y-intercept of the function is at x=0
So, Put x=0 in the equation [tex]f(x)=x^2-8x+5[/tex]
[tex]f(0)=0^2-8(0)+5[/tex]
[tex]y=5[/tex]
The y-intercept of the function is (0,5).
The 'd' statement is true.
To find the function crosses the x-axis twice refer the attached figure below.
Yes the function crosses the x-axis twice.
The 'e' statement is true.
