Question Video: Given a Graph of a Quadratic Function Identify the Coordinates of the Vertex | Nagwa Question Video: Given a Graph of a Quadratic Function Identify the Coordinates of the Vertex | Nagwa

# Question Video: Given a Graph of a Quadratic Function Identify the Coordinates of the Vertex Mathematics • Third Year of Preparatory School

## Join Nagwa Classes

Identify the coordinates of the vertex of the quadratic function π(π₯) = π₯Β² β 1.

01:34

### Video Transcript

Identify the coordinates of the vertex of the quadratic function π of π₯ equals π₯ squared minus one.

Weβre given the quadratic function π of π₯ equals π₯ squared minus one and the graph of that function. First, we should recall what the vertex of a quadratic function is. The vertex is either a minimum or a maximum, sometimes called the turning point. Since this parabola opens upward, the vertex will be a minimum. By inspection, it looks like we can see the minimum here at an π₯-coordinate of zero and a π¦-coordinate of negative one, halfway between zero and negative two.

Sometimes weβre not able to identify the vertex of a function from its graph with accuracy, so itβs helpful to know another method for finding this. For a given function in vertex form π¦ equals π times π₯ minus β squared plus π. The vertex of the graph is located at β, π. We can rearrange the function we were given so that itβs in vertex form. π of π₯ equals one times π₯ minus zero squared plus negative one. This means that π equals one, β equals zero, and π equals negative one. Since the vertex is the point β, π, that would be equal to zero, negative one.

This matches what we see on the graph that the vertex of the function π of π₯ equals π₯ squared minus one is located at the point zero, negative one.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions