Converting Quadratic Equations: The Vertex Form Explained

vertex form of a quadratic equation

The vertex form of a quadratic equation is a way to express a quadratic equation in the form of

y = a(x – h)^2 + k

where (h, k) represents the coordinates of the vertex of the parabola, and “a” is a non-zero coefficient that determines the direction and width of the parabola

The vertex form of a quadratic equation is a way to express a quadratic equation in the form of

y = a(x – h)^2 + k

where (h, k) represents the coordinates of the vertex of the parabola, and “a” is a non-zero coefficient that determines the direction and width of the parabola.

To convert a quadratic equation from standard form (y = ax^2 + bx + c) to vertex form, you can follow these steps:

Step 1: Determine the values of “h” and “k”
The values of “h” and “k” can be found using the following formulas:
– The x-coordinate of the vertex, h, can be found using the formula: h = -b / (2a)
– The y-coordinate of the vertex, k, can be found by substituting the value of “h” back into the equation as k = f(h), where f(x) is the given quadratic equation.

Step 2: Plug the values of “h” and “k” into the vertex form equation
Once you have determined the values of “h” and “k” from Step 1, substitute them into the vertex form equation y = a(x – h)^2 + k. This will give you the equation in vertex form.

For example, let’s say we have the quadratic equation y = 2x^2 + 4x + 3 in standard form.

Step 1: Determine the values of “h” and “k”
Using the formula h = -b / (2a), we can calculate h as follows:

h = -4 / (2 * 2) = -1

Next, substitute the value of h back into the equation to get k:

k = f(h) = 2(-1)^2 + 4(-1) + 3 = 2 + (-4) + 3 = 1

So, the vertex of the parabola is (-1, 1).

Step 2: Plug the values of “h” and “k” into the vertex form equation
Substituting the values of h = -1 and k = 1 into the vertex form equation y = a(x – h)^2 + k, we get:

y = a(x + 1)^2 + 1

This is the quadratic equation in vertex form.

Please note that the value of “a” in the vertex form equation represents the stretch or compression factor of the parabola. It is not directly obtained from the standard form equation, but can be determined using additional information or by graphing the parabola.

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