The function is graphed in the -plane. What is the vertex of the graph of ?
When a quadratic is given in vertex form , immediately recall that the vertex is and then carefully identify and by matching the expression to . Pay special attention to the signs: inside the parentheses the pattern is , so if you see then , and the number added or subtracted outside is . This lets you read off the vertex in a few seconds without expanding or doing any extra algebra.
Hints
Identify the form of the quadratic
Look at how the function is written: . Does this match a standard pattern you know for quadratics, like vertex form?
Recall what the vertex form tells you
For a function in the form , what point does this form give you on the graph?
Match the given function to the pattern carefully
In , think about what and must be in . Pay close attention to the minus sign inside the parentheses and the minus sign on the constant term.
Desmos Guide
Enter the function
Type y = (x - 2)^2 - 3 into Desmos to graph the quadratic.
Locate the vertex on the graph
Zoom or pan if needed, then move your cursor along the parabola; Desmos will highlight the minimum point (the vertex) and show its coordinates. Those coordinates are the answer.
Step-by-step Explanation
Recognize the vertex form of a quadratic
A quadratic written as is in vertex form. For any quadratic in this form, the vertex of its graph is the point .
Match the given function to the vertex form
The given function is
Compare this to :
- Inside the parentheses you have , which matches , so .
- Outside, you have added, which matches , so .
Write the coordinates of the vertex
Since the vertex of is and here and , the vertex of the graph of is .