Question

Which equation has a vertex of (-4, 5)?(1 point) Responses y=(x−4)2+5 𝑦 = ( 𝑥 − 4 ) 2 + 5 y is equal to open paren x minus 4 close paren squared plus 5 y=(x+4)2−5 𝑦 = ( 𝑥 + 4 ) 2 − 5 y is equal to open paren x plus 4 close paren squared minus 5 y=(x+4)2+5 𝑦 = ( 𝑥 + 4 ) 2 + 5 y is equal to open paren x plus 4 close paren squared plus 5 y=(x−4)2−5

Answer 1

The vertex form of a quadratic equation is given by:

\[ y = a(x - h)^2 + k \]

where \((h, k)\) is the vertex of the parabola.

In this case, the vertex is given as \((-4, 5)\). Thus, we have:

• \(h = -4\)
• \(k = 5\)

Substituting these values into the vertex form of the equation, we get:

\[ y = a(x + 4)^2 + 5 \]

Since none of the options provided indicate the value of \(a\), we can see that the correct format should be \(y = (x + 4)^2 + 5\).

Among the responses, the correct equation is:

\[ y = (x + 4)^2 + 5 \]

So the answer is:

\(y = (x + 4)^2 + 5\).