Question

Please help with this algebra ii question

Answer 1

B


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Hope this helps you

Answer 2

Answer:

Second Choice

Step-by-step explanation:

The vertex form can be expressed as:

$\displaystyle \large{f(x) = a {(x - h)}^{2} + k}$

We know that the vertex is (h,k) which we are given (-3,-1). Substitute h = -3 and k = -1 in:

$\displaystyle \large{f(x) = a {(x - ( - 3))}^{2} - 1} \\ \displaystyle \large{f(x) = a {(x + 3)}^{2} - 1}$

Now we know that the parabola passes through (-2,1). Substitute x = -2 and f(x) = 1 then solve for a.

$\displaystyle \large{1= a {( - 2 + 3)}^{2} - 1} \\ \displaystyle \large{1= a {(1)}^{2} - 1} \\ \displaystyle \large{1= a - 1} \\ \displaystyle \large{1 + 1= a } \\ \displaystyle \large{2 = a}$

Therefore a = 2.

Hence:-

$\displaystyle \large{f(x) = 2{(x + 3)}^{2} - 1}$