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What is the vertex form of the equation graphed below?



(1 point)
Responses

y=−2(x+1)2−3
y is equal to negative 2 times open paren x plus 1 close paren squared minus 3

y=3(x−1)2+3
y is equal to 3 times open paren x minus 1 close paren squared plus 3

y=3(x+1)2−3
y is equal to 3 times open paren x plus 1 close paren squared minus 3

y=−2(x−1)2+3

1 answer

To determine the vertex form of the equation based on the given options, let's analyze the structure of vertex form, which is generally given as:

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

where \((h, k)\) is the vertex of the parabola and \(a\) indicates the direction and the width of the parabola.

Here's the breakdown of the given options:

  1. \(y = -2(x + 1)^2 - 3\)

    • Vertex: \((-1, -3)\)
    • Opening: Downwards (since \(a = -2\))

  2. \(y = 3(x - 1)^2 + 3\)

    • Vertex: \((1, 3)\)
    • Opening: Upwards (since \(a = 3\))

  3. \(y = 3(x + 1)^2 - 3\)

    • Vertex: \((-1, -3)\)
    • Opening: Upwards (since \(a = 3\))

  4. \(y = -2(x - 1)^2 + 3\)

    • Vertex: \((1, 3)\)
    • Opening: Downwards (since \(a = -2\))

Without the graph, it's challenging to select the correct equation, but you can identify the vertex coordinate and the direction of the opening by comparing the vertices and the value of \(a\).

To determine the correct equation, check these against the graph's vertex and the direction in which the parabola opens. If the graph shows a vertex at \((-1, -3)\) and opens downwards, then the match is the first option:

\[ y = -2(x + 1)^2 - 3 \]

If it opens upwards with a vertex at \((1, 3)\), then either the second or the fourth options would be applicable, depending on their vertex coordinates.

Please provide the vertex or direction of the graph if you need further assistance in selecting the correct option!