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Using the vertex (5, 17) and a point (11, -109), write your equation in Vertex Form.

1 Answer

3 votes

Answer:

y=-3.5(x−5)^2+17

Explanation:

Let's assume that since this equation has a vertex that it is a parabola with the form y = ax^2 + bx + c.

Let's rewrite it in vertex form as:

y=a(x−h)^2+k

where h and k are the horizontal (h) and vertical (k) coordinates of the vertex.

The vertex of (5,17) gives us both h (5) and k (17), Substituting these values gives us:

y=a(x−5)^2+17

To find a, use the one given point the parabola intersects (11,-109) and solve for a:

y=a(x−5)^2+17

-109=a((11)−5)^2+17

-109=a(6)^2+17

-109-17=a(36)

36a = -126

a = -3.5

This leads us to:

y=-3.5(x−5)^2+17

See the attached graph.

Using the vertex (5, 17) and a point (11, -109), write your equation in Vertex Form-example-1
User TjeerdJan
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