Question

Which response is the correct way to write the equation in vertex form for the function?
(-4, 2)
(1 point)
Responses

y=−1/4(x+4)2+2

y=−1/4(x−2)2+4

y=−1/4(x−4)2+2

y=−1/4(x+2)2+4

Answer 1

To convert a quadratic equation into vertex form \( y = a(x-h)^2 + k \), you need the vertex \((h, k)\) of the parabola. In this case, you have the vertex at \((-4, 2)\), meaning \(h = -4\) and \(k = 2\).

The primary expression we need is:
\[ y = a(x + 4)^2 + 2 \]
where \( a \) is the coefficient that dictates the width and direction of the parabola.

However, from the given options, it seems you are given a fixed value for \( a \), which is \(-1/4\).

Thus, substituting \( h = -4 \) and \( k = 2 \) into the vertex form gives:
\[ y = -\frac{1}{4}(x + 4)^2 + 2 \]

So the correct response is:
**y = -1/4(x + 4)² + 2**.