Math  /  Algebra

QuestionWrite an equation for the function graphed above. g(v)=(v2)2+4g(v)=-(v-2)^{2}+4
Round to 4 decimal places as needed.

Studdy Solution

STEP 1

1. The graph is a parabola, which is a quadratic function.
2. The vertex form of a parabola is given by g(v)=a(vh)2+k g(v) = a(v-h)^2 + k , where (h,k)(h, k) is the vertex.
3. The parabola opens downward, indicating that the coefficient a a is negative.
4. The vertex of the parabola is at the point (2, 4).

STEP 2

1. Identify the vertex of the parabola.
2. Determine the direction the parabola opens.
3. Write the equation in vertex form.
4. Verify the equation matches the graph.

STEP 3

Identify the vertex of the parabola. From the image description, the vertex is at the point (2, 4).

STEP 4

Determine the direction the parabola opens. The graph is described as a downward-opening parabola, which means the coefficient a a is negative.

STEP 5

Write the equation in vertex form. The vertex form of a parabola is:
g(v)=a(vh)2+k g(v) = a(v-h)^2 + k
Substitute the vertex (h,k)=(2,4)(h, k) = (2, 4) into the equation:
g(v)=a(v2)2+4 g(v) = a(v-2)^2 + 4
Since the parabola opens downward, a a is negative. The provided equation is:
g(v)=(v2)2+4 g(v) = -(v-2)^2 + 4

STEP 6

Verify the equation matches the graph. The equation g(v)=(v2)2+4 g(v) = -(v-2)^2 + 4 has a vertex at (2, 4) and opens downward, which matches the description of the graph.
The equation for the function graphed is:
g(v)=(v2)2+4 g(v) = -(v-2)^2 + 4

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