# How do you write a quadratic equation in standard form to vertex form?

## How do you write a quadratic equation in standard form to vertex form?

We can try to convert a quadratic equation from the standard form to the vertex form using completing the square method:

1. Write the parabola equation in the standard form: y = a*x² + b*x + c ;
2. Extract a from the first two terms: y = a * (x² + b/a * x) + c ;
3. Complete the square for the expressions with x .

### How do you find the quadratic function?

A = 2xy = 2x (400 -4x/3). We need to find the value of x that makes A as large as possible. A is a quadratic function of x, and the graph opens downward, so the highest point on the graph of A is the vertex. Since A is factored, the easiest way to find the vertex is to find the x-intercepts and average.

How do you write a quadratic function in standard form?

The standard form of a quadratic function is f(x)=a(x−h)2+k. The vertex (h,k) is located at h=–b2a,k=f(h)=f(−b2a).

How do you write a quadratic equation?

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b and c being constants, or numerical coefficients, and x being an unknown variable.

## What is the vertex form of a quadratic function?

The vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a, h, and k are constants.

### How do you find the quadratic equation of a parabola?

The graph of a quadratic function is a parabola.

1. The general form of a quadratic function is f(x)=ax2+bx+c where a, b, and c are real numbers and a≠0.
2. The standard form of a quadratic function is f(x)=a(x−h)2+k.
3. The vertex (h,k) is located at h=–b2a,k=f(h)=f(−b2a).

How do you write a parabola equation in vertex form?

Step 1. Find the vertex and one other point. The vertex is (3, 1) and another point on the graph is (5, 9). Step 2. Substitute the vertex and point into the formula and solve for the a -value. Step 3. Write the equation of the parabola in vertex form.

How do you find the vertex of a quadratic function?

Given a quadratic function f ( x) = a x 2 + b x + c, depending on the sign of the x 2 coefficient, a, its parabola has either a minimum or a maximum point: in either case the point (maximum, or minimum) is known as a vertex . To find the vertex we calculate its x -coordinate, h, with the formula given below.

## What is the x-coordinate of the vertex of the parabola?

Since 2 > 0 this parabola’s vertex is a minimum point . So the x -coordinate of the vertex is h = 1 . Step 2: we calculate the y -coordinate of the vertex by replacing x by 1 inside y = 2 x 2 − 4 x − 6 and calculating the value of y. So the y -coordinate of the vertex is k = − 8 .

### How to find a quadratic equation from a graph with 2 points?

In order to find a quadratic equation from a graph using only 2 points, one of those points must be the vertex. With the vertex and one other point, we can sub these coordinates into what is called the “vertex form” and then solve for our equation. The vertex formula is as follows, where (d,f) is the vertex point and (x,y) is the other point: