# How do you find the vertex of a parabola given the axis of symmetry?

## How do you find the vertex of a parabola given the axis of symmetry?

The Vertex Form of a quadratic function is given by: f(x)=a(x−h)2+k , where (h,k) is the Vertex of the parabola. x=h is the axis of symmetry. Use completing the square method to convert f(x) into Vertex Form.

## How do you find the vertex of the axis?

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 .

How do I find the y-intercept of a parabola?

We can use this fact to find the y-intercepts by simply plugging 0 for x in the original equation and simplifying. Notice that if we plug in 0 for x we get: y = a(0)2 + b(0) + c or y = c. So the y-intercept of any parabola is always at (0,c).

What is the Y intercept of a parabola equation?

The y-intercept of any graph is a point on the y-axis and therefore has x-coordinate 0. We can use this fact to find the y-intercepts by simply plugging 0 for x in the original equation and simplifying. Notice that if we plug in 0 for x we get: y = a(0)2 + b(0) + c or y = c.

### What does a mean in Y a XH 2 K?

vertex
The vertex form of a quadratic is given by. y = a(x – h)2 + k, where (h, k) is the vertex. The “a” in the vertex form is the same “a” as.

### What is the Y-intercept of a parabola equation?

What is the vertex of the graph of y x2?

(0, 0)
In the graph of y = x2, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward.

How do you find the y-intercept in a quadratic function?

Finding the y-intercept in a quadratic function The standard form of a quadratic equation is written as y=ax2+bx+c, where x and y are variables and a, b, and c are known constants. To find the y-intercept from a quadratic equation, substitute 0 as the value for x and solve.

#### How do you calculate the vertex of a parabola?

But the equation for a parabola can also be written in “vertex form”: y = a ( x − h ) 2 + k. In this equation, the vertex of the parabola is the point ( h , k ) . You can see how this relates to the standard equation by multiplying it out: y = a ( x − h ) ( x − h ) + k y = a x 2 − 2 a h x + a h 2 + k .

What is the standard equation for a parabola?

The “general” form of a parabola’s equation is the one you’re used to, y = ax2 + bx + c — unless the quadratic is “sideways”, in which case the equation will look something like x = ay2 + by + c.

What is the definition of a vertex of a parabola?

The Vertex of a Parabola. The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x 2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.

## How does vertex form work?

(h,k) is the vertex as you can see in the picture below

• If a is positive then the parabola opens upwards like a regular “U”.
• If a is negative,then the graph opens downwards like an upside down “U”.
• If|a|< 1,the graph of the parabola widens.
• If|a|> 1,the graph of the graph becomes narrower (The effect is the opposite of|a|< 1).