Question

ng % +24-1 - 10.x - 30 10) S (1) = -x? - 17 are ministere maxleng due 11) f(x) = 32 - 54x + 241 Identify the vertex, axis of symmetry, and min/max value of each. 1272 18.X +86.18312)

Answer 1

`f(x)=x^2\text{ + 4x +5}`

Step 1:

To get the vertex

`\begin{gathered} x^2\text{ + 4x + 4 + 1} \\ (x^2+4x+4)\text{ + 1} \\ (x+2)^2\text{ + 1} \end{gathered}`

Comparing this to the equation in the vertex form

`f(x)=a(x-h)^2\text{ + k}`

-h = 2

h= -2

k =1

So the vertex is (h,k) = (-2, 1)

The axis of symmetry is at -2

The minimum value can be obtained from the equation

`\begin{gathered} (4ac-b^2)/(4a) \\ \frac{4*1*5-4^2}{4\text{ x 1}} \\ (20-16)/(4) \\ (4)/(4) \\ =1 \end{gathered}`

The vertex is (-2, 1)

The axis of symmetry is at -2

The minimum value is 1 ( i.e coordinate (-2,1)