Find the Quadratic Function with Minimum Point (-2,0): Parabola Identification

Question

Which function corresponds to a parabola with a minimum point of $(-2,0)$ ?

00:00 Find the appropriate function for the parabola with the minimum point

00:03 A smiling parabola has a positive coefficient for X squared

00:06 In this parabola, the intersection point is at the origin

00:10 We need a sad parabola 2 steps to the left

00:21 Negative times negative always equals positive

00:27 And this is the solution to the question

To solve the problem, we need to write the equation of a parabola with the given vertex.

Step 1: Identify the form of the equation. For a parabola with vertex $(h, k)$ , the equation is $y = (x - h)^2 + k$ .

Step 2: Plug in the coordinates of the vertex. Here, the vertex is $(-2, 0)$ , so $h = -2$ and $k = 0$ .

Step 3: Substitute into the vertex form:

Step 4: Simplify the equation.

This results in:

Therefore, the function corresponding to the given parabola is $y = (x + 2)^2$ .

$y=(x+2)^2$