Unit 4 · Quadratic Functions4.2
Vertex and Roots of a Parabola
Topic The graph of f(x) = ax² + bx + c is a parabola. It opens upwards when a > 0 and downwards when a < 0. Its vertex T(r, k) is given by r = −b/2a and k = f(r), and the graph is symmetric about the line x = r.
Figure Figure 4.2 The graph of f(x) = x² − 2x − 3
Example Example 5 for f(x) = x² − 2x − 3: r = 1, k = −4·roots x = −1 and x = 3
96 11th Grade MathematicsSchool publication
Activity Activity 4
Match the functions with their vertices.
| x² − 2x | (0, 4) |
| x² + 4 | (2, 0) |
| −x² + 6x | (1, −1) |
| (x − 2)² | (3, 9) |
Exercises
Question 12.What is the x-coordinate of the vertex of the parabola f(x) = x² − 6x + 5?
A) −3B) 2C) 3D) 5
Question 13.At which points does the parabola y = −x² + 4 cross the x-axis?
A) ±1B) ±2C) ±4D) 0 and 4
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