fine the equation of the parabola with vertex at (2,5) and also passes through (0,-11)

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madeleinejames20 · Accepted Answer

To find the equation of a parabola with a vertex at (2,5) and passing through the point (0,-11), we can use the vertex form of a parabolic equation.
The vertex form of a parabola is given by:

y = a (x - h)^{2} + k

Where (h, k) represents the coordinates of the vertex.
Given that the vertex is (2,5), we have h = 2 and k = 5.
Substituting these values into the equation, we have:

y = a (x - 2)^{2} + 5

Now, we need to determine the value of a. To do that, we can use the fact that the parabola passes through the point (0,-11).
Substituting x = 0 and y = -11 into the equation, we get:

- 11 = a (0 - 2)^{2} + 5

Simplifying further:

- 11 = a (- 2)^{2} + 5

- 11 = 4 a + 5

Next, we isolate the term with 'a' on one side of the equation:

4 a = - 11 - 5

4 a = - 16

Finally, we solve for 'a' by dividing both sides of the equation by 4:

a = \frac{- 16}{4}

a = - 4

Now that we have the value of 'a', we can substitute it back into the equation:

y = - 4 (x - 2)^{2} + 5

Therefore, the equation of the parabola with a vertex at (2,5) and passing through the point (0,-11) is:

y = - 4 (x - 2)^{2} + 5

fine the equation of the parabola with vertex

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