Question

What equation is used to find the vertex form of a parabola with the vertex (h, k)? (5 points)

Answer 1

In the vertex form
`\(y = a(x - h)^2 + k\)`, the coordinates
`\((h, k)\)` denote the vertex of the parabola.
`\(h\)` defines the horizontal shift, and
`\(k\)` determines the vertical shift from the standard position. Thus,
`\((h, k)\)` marks the vertex.

The equation of a parabola in vertex form is given by:

`\[y = a(x - h)^2 + k\]`

To show that the point
`\((h, k)\)` is the vertex using this equation, we can compare it to the standard vertex form equation
`\(y = a(x - h)^2 + k\)`, where
`\((h, k)\)` are the coordinates of the vertex.

The vertex of the parabola occurs at the point
`\((h, k)\).` Here's how:

Comparison to the Standard Form:

The equation
`\(y = a(x - h)^2 + k\)` directly involves the parameters
`\(h\)` and
`\(k\)` in the equation.

The term
`\((x - h)^2\)`in the equation represents horizontal shifts. Setting
`\(x = h\)` gives
`\(y = a(0)^2 + k = k\)`, confirming that when
`\(x = h\)`, the corresponding
`\(y\)` value is
`\(k\)`, which represents the vertical position of the vertex.

Hence, at
`\(x = h\)`, the y-coordinate is
`\(k\)`, which confirms that
`\((h, k)\)`is the vertex.

Explanation of (h) and (k):

(h) represents the horizontal shift or displacement of the parabola from the standard position along the x-axis.

(k) represents the vertical shift or displacement of the entire parabola from the standard position along the y-axis.

complete the question

Why (h, k) is the Vertex in the Vertex Form of a Parabola y=a(x−h)2+k

the vertex?