Question

Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Check all that apply.

Answer 1

Answer:

Option a,d and e are true statements.  

Step-by-step explanation:

Given : Function $f(x)=x^2-8x+5$

To find : Which statements are true about the graph of the function, Check all that apply?

Solution :  

The quadratic function is in the form, $y=ax^2+bx+c$

The vertex form is $y=a(x-h)^2+k$

To find vertex form we apply completing the square,

$f(x)=x^2-8x+5+4^2-4^2$

$f(x)=x^2-8x+(4)^2+5-16$

$f(x)=(x-4)^2-11$

The vertex form of the function is $f(x)=(x-4)^2-11$

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. $x=-\frac{b}{2a}$ is the axis of symmetry,

So, $x=-\frac{-8}{2(1)}$

$x=4$

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 $f(x)=x^2-8x+5$

$f(0)=0^2-8(0)+5$

$y=5$

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.

Answer 2

D. The y-intercept of the function is (0, 5) and e. The function crosses the x-axis twice are true