Math  /  Algebra

QuestionFor the quadratic function f(x)=x2+2x+1f(x)=x^{2}+2 x+1, answer parts (a) through (f)(f). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down.
The vertex is (1,0)(-1,0). (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is x=1x=-1. (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the yy-intercept and the xx-intercepts, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The xˉ\bar{x}-intercept(s) is/are \square . (Type an integer or a simplified Yaction. Use a comma to separate answers as needed.) B. There are no xx-intercepts.

Studdy Solution
To find the x x -intercepts, set f(x)=0 f(x) = 0 and solve for x x .
The equation becomes x2+2x+1=0 x^2 + 2x + 1 = 0 .
This can be factored as (x+1)2=0 (x + 1)^2 = 0 .
Solving gives x+1=0 x + 1 = 0 , so x=1 x = -1 .
Thus, there is one x x -intercept at (1,0) (-1, 0) .
The solutions are: (a) Vertex: (1,0)(-1, 0), Axis of symmetry: x=1x = -1, Concave up. (b) y y -intercept: (0,1)(0, 1), x x -intercept: (1,0)(-1, 0).

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