# How do you find a quadratic equation with points and axis of symmetry?

## How do you find a quadratic equation with points and axis of symmetry?

How do i find the equation of a parabola given 2 points and the axis of symmetry, but no vertex?

- Using the vertex form of a parabola f(x) = a(x – h)2 + k where (h,k) is the vertex of the parabola.
- The axis of symmetry is x = 0 so h also equals 0.
- a = 1.
- Substituting the a value into the first equation of the linear system:

## What is the axis of symmetry in a function?

The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line splits the graph of a quadratic equation into two mirror images.

**How do you find the axis of symmetry in standard form?**

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

**What is axis of symmetry of a line segment?**

more A line through a shape so that each side is a mirror image. When the shape is folded in half along the axis of symmetry, then the two halves match up.

### What is axis of symmetry of a triangle?

A line of symmetry for a triangle must go through one vertex. The two sides meeting at that vertex must be the same length in order for there to be a line of symmetry. Finally, the triangle with side lengths 3,5,5 has one line of symmetry through the vertex where the two sides of length 5 meet.

### What is an example of a line of symmetry?

For example, take your face. When we draw a line down our face exactly at the centre, then the left side of our face is symmetric to our right side of the face. This defines symmetry. This line that divides a figure or shape or any image in identical halves then that figure is said to have a line symmetry.

**How to write the axis of symmetry of a quadratic equation?**

Use the values of the coefficients to write the equation of axis of symmetry. The graph of a quadratic equation in the form y = ax2 + bx + c has as its axis of symmetry the line x = − b 2a . So, the equation of the axis of symmetry of the given parabola is x = − ( 5) 2 ( − 2) or x = 5 4 .

**Which is the standard form of the quadratic function y?**

Figure 5.1.5: Graph of a parabola showing where the x and y intercepts, vertex, and axis of symmetry are for the function y = − 3(x + 2)2 + 4. The standard form is useful for determining how the graph is transformed from the graph of y = x2.

#### When does the axis of symmetry pass through the vertex?

The axis of symmetry always passes through the vertex of the parabola. The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y = a x 2 + b x + c, the axis of symmetry is a vertical line x = − b 2 a. Example 1:

#### How to write the axis of symmetry of a parabola?

The parabola opens “sideways” and the axis of symmetry of the parabola is horizontal. The standard form of equation of a horizontal parabola is x = ay2 + by + c . . . Use the values of the coefficients to write the equation of axis of symmetry.