Question

The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the graph?
(−9, −2)
(−17, −2)
(−2, −17)
(−2, −9)

Answer 1

Answer:

D) $(-2,-9)$

Step-by-step explanation:

Vertex Form of a Vertical Parabola:

$y=a(x-h)^2+k$

Vertex -> $(h,k)$

Axis of Symmetry -> $x=h$

Vertical Scale Factor -> $a$

• To turn $f(x)=x^2+4x-5$ into vertex form, we need to complete the square on the right side
• Therefore, if $f(x)=0$, then $0+9=x^2+4x-5+9$ completes the square on the right side
• This becomes $9=(x+2)^2$
• This means that our function in vertex form is $f(x)=(x+2)^2-9$

Therefore, the vertex of the graph is $(h,k)=(-2,-9)$.