Question 97·Easy·Nonlinear Functions
The function is defined by . What is the -coordinate of the vertex of the graph of in the -plane?
(Express the answer as an integer)
When a quadratic is already in vertex form , immediately read the vertex as —no extra algebra is needed. Pay close attention to signs: if the expression is , rewrite mentally as so you clearly see and , then answer using the coordinate the question asks for (x or y) without mixing them up.
Hints
Think about the form of the quadratic
Is the function written in a way that immediately shows the vertex, like ? If so, how do and relate to the vertex?
Match pieces of the function
Compare to . What number plays the role of ? What number plays the role of ?
Focus on the constant term outside the square
In vertex form, the y-coordinate of the vertex is the constant added or subtracted outside the squared expression. What is that constant in ?
Desmos Guide
Enter the function
In Desmos, type g(x) = (x + 3)^2 - 4 to graph the function.
Find the vertex and read its y-coordinate
Tap or click on the lowest point of the parabola (its vertex). Desmos will display the vertex as a point ; the y-value shown there is the y-coordinate of the vertex you need.
Step-by-step Explanation
Recall the vertex form of a quadratic
A quadratic function in vertex form looks like
In this form, the vertex of the parabola is the point , where is the x-coordinate and is the y-coordinate.
Match the given function to vertex form
The given function is
Rewrite the inside of the square as :
Now it clearly matches with , , and .
Identify the y-coordinate of the vertex
From the vertex form , the vertex is . Here, , so the y-coordinate of the vertex is .