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BUILD PERSEVERANCE Enter an equation in vertex form for a quadratic function g(x) that has its vertex at (−4, 8) and crosses the x-axis at (−6, 0) and (−2, 0) .

Plese help.

Respuesta :

sqdancefan

Answer:

  g(x) = -2(x +4)² +8

Step-by-step explanation:

You want the vertex form equation of the quadratic with vertex (-4, 8) and x-intercepts (-6, 0) and (-2, 0).

Vertex form

The vertex form of the quadratic equation is ...

  g(x) = a(x -h)² +k . . . . . . . . . vertex (h, k), vertical scale factor 'a'

The given vertex tells us the equation is ...

  g(x) = a(x +4)² +8 . . . . . . for some value of 'a'

Scale factor

Using the point (-6, 0), we can find 'a':

  0 = a(-6 +4)² +8 = 4a +8

  a = -8/4 = -2 . . . . . . . . . . . . solve for 'a'

The required equation is ...

  g(x) = -2(x +4)² +8

Ver imagen sqdancefan
marmar58

Answer:

hope this helps:3

Step-by-step explanation:

Let's start by identifying the parameters of the equation. The vertex of a quadratic function is its turning point, where the graph of the equation changes direction either from increasing to decreasing or from decreasing to increasing. The vertex is marked by the coordinates of its minimum or maximum value on the x-axis. In this case, the vertex of the graph is located at (−4, 8).

Next, we know that the graph of the quadratic function crosses the x-axis at[]{−6, 0) and ${\displaystyle {-2,0}.}

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