Nonlinear Relationship Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardFor \(f(x) = x^2 - 4x + 3\), find the vertex and determine whether the parabola opens up or down.
Solution
- 1 The coefficient of \(x^2\) is 1 > 0, so the parabola opens upward.
- 2 Vertex x-coordinate: \(x = -\frac{b}{2a} = -\frac{-4}{2 \cdot 1} = 2\).
- 3 Vertex y-value: \(f(2) = 4 - 8 + 3 = -1\).
- 4 Vertex: \((2, -1)\). This is the minimum.
Answer
Vertex: \((2, -1)\); opens upward
For \(ax^2+bx+c\), the vertex is at \(x=-b/(2a)\). With \(a>0\) the parabola opens up and the vertex is a minimum.
About Nonlinear Relationship
A relationship between two quantities where the rate of change is not constant—the graph is curved, not a straight line.
Learn more about Nonlinear Relationship →More Nonlinear Relationship Examples
Example 1 medium
The area of a square is (A = x^2). Compare how (A) changes when (x) goes from 1 to 2, then 2 to 3. I
Example 3 mediumFor (y = x^2), calculate values at (x = -2, -1, 0, 1, 2). Is the graph symmetric?
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