How do you find the equation of the parabola in vertex form?

How to find a parabola’s equation using its Vertex Form

Table of Contents

Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola’s equation in the form: y=a(x−h)2+k.
Step 2: find the value of the coefficient a by substituting the coordinates of point P into the equation written in step 1 and solving for a.

What is vertex parabola?

The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry. For a parabola whose equation is given in standard form , the vertex will be the minimum (lowest point) of the graph if and the maximum (highest point) of the graph if .

What is vertex form of a parabola?

The Vertex formula of a parabola is used to find the coordinates of the point where the parabola crosses its axis of symmetry. The vertex is the point (h,k). As we know the standard equation of a parabola is y = ax2+bx+c.

How do you write a parabola in vertex form?

(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”.

What is the formula for the vertex of a parabola?

The maximum or minimum value of the parabola is called its vertex.

A vertical line passing through the vertex is called the axis of symmetry for the parabola.

The point where the parabola crosses the y -axis is called the y-intercept.

How to find equation of a parabola?

radar dishes or communication satellite

satellite dishes

the reflector on torches and spotlights

focusing the sun’s rays to make a hot spot

How to put equations of parabolas in standard form?

(h,k) is the vertex

If a is positive then the parabola opens upwards like a regular “U”. (same as standard form)

If a is negative,then the graph opens downwards like an upside down “U”. (same as standard form)

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).

How do you find the equation of the parabola in vertex form?