Write the quadratic function in vertex form: f(x)=

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For the given roots -7,5 write the quadratic equation in standard form using function notation

To write the quadratic function in vertex form, we need the general form of a quadratic equation: f(x) = ax^2 + bx + c.

To convert it to vertex form, we follow these steps:

Step 1: Complete the square for the x terms in the equation.

Rewrite the equation as f(x) = a(x^2 + (b/a)x) + c.

Step 2: Take half of the coefficient of x (which is b/a), square it, and add it to both sides of the equation.

f(x) + (b/2a)^2 = a(x^2 + (b/a)x + (b/2a)^2) + c.

Step 3: Rewrite the quadratic expression inside the parentheses as a perfect square trinomial.

f(x) + (b/2a)^2 = a(x + b/2a)^2 + c.

Step 4: Simplify the equation.

f(x) + (b/2a)^2 = a(x + b/2a)^2 + c

f(x) + (b/2a)^2 - c = a(x + b/2a)^2

Step 5: Rewrite the equation in vertex form.

The vertex form of the quadratic equation is f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.

So, the quadratic function in vertex form is:

f(x) = a(x + b/2a)^2 + c - (b/2a)^2

To write a quadratic function in vertex form, we use the formula:

f(x) = a(x - h)^2 + k

Where (h, k) represents the coordinates of the vertex, and a is a constant that affects the shape and direction of the parabola.

To find the vertex form of the quadratic function, we need to know the values of a, h, and k.

If you already have a quadratic function in standard form (f(x) = ax^2 + bx + c), you can use the following steps to convert it into vertex form:

Step 1: Identify the values of a, b, and c from the standard form equation.

Step 2: Find the x-coordinate of the vertex using the formula: h = -b / (2a).

Step 3: Substitute the value of h into the standard form equation to find the corresponding y-coordinate, which is the value of k.

Step 4: Plug the values of a, h, and k into the vertex form equation (f(x) = a(x - h)^2 + k) to get the quadratic function in vertex form.

By using these steps, you can convert any quadratic function from standard form to vertex form.