Write a quadratic function from its vertex and another point

Answer:

y = (-2)(x + 2)^2 - 4.

Step-by-step explanation:

The vertex form of a quadratic function is in the form

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

where

  • a is a coefficient that needs to be found, and
  • (h, k) is the vertex of this function.

In this question, the vertex of this quadratic function is at the point (-2, -4). In other words, h = (-2) and k = (-4). Substitute these value into the general equation:

y = a (x - (-2))^2 +(- 4).

Simplify to obtain:

y = a (x + 2)^2 - 4.

The only missing piece here is the coefficient a. That’s likely why the problem gave (-1, -6), yet another point on this quadratic function. If this function indeed contains the point (-1, -6), y should be equal to (-6) when x = (-1). That is:

-6 = a(-1 + 2)^2 -4.

Solve this equation for a:

a = -6 - (-4) = -2.

Hence the equation of the quadratic function in its vertex form:

y = (-2)(x + 2)^2 - 4.

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