Math Problem Statement

graph the quadratic equation f(x)=(x-1)^2

Solution

Here is the graph of the quadratic function f(x)=(x1)2f(x) = (x - 1)^2. The parabola has its vertex at (1,0)(1, 0), and it opens upward.

Do you want any further details or have any questions?

Here are five related questions you might find useful:

  1. How do you find the vertex of a general quadratic function?
  2. What is the significance of the axis of symmetry in a parabola?
  3. How would the graph change if the function was f(x)=(x1)2f(x) = -(x - 1)^2?
  4. Can you determine the y-intercept algebraically?
  5. How would this function shift if we added a constant to it, say f(x)=(x1)2+3f(x) = (x - 1)^2 + 3?

Tip: The vertex form of a quadratic function makes it easy to identify shifts, direction, and the vertex of the parabola.

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Graphing Parabolas
Vertex Form

Formulas

f(x) = (x - h)^2 + k
Standard form of a quadratic function: ax^2 + bx + c

Theorems

Vertex Form Theorem
Axis of Symmetry

Suitable Grade Level

Grades 9-10