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 grap
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, fi your choice. A. The xx-intercept(s) is/are -1 . \square (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no xx-intercepts.
What is the yy-intercept? Select the correct choice below and, if necessary, fill in the answer box to com A. The yy-intercept is 1 . \square (Type an integer or a simplifed fraction.) B. There is no y-intercept. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. \square (d) Find the domain and the range of the quadratic function.
The domain of ff is \square 7. (Type your answer in interval notation.)

Studdy Solution
The domain of any quadratic function is all real numbers, so the domain of f f is: (,) (-\infty, \infty)
The range of the function is determined by the vertex and the direction of the parabola. Since the parabola opens upwards and the vertex is at (1,0)(-1, 0), the range is: [0,) [0, \infty)
The vertex is (1,0)(-1, 0), the axis of symmetry is x=1 x = -1 , the graph is concave up, the y y -intercept is (0,1)(0, 1), the x x -intercept is (1,0)(-1, 0), the domain is (,)(-\infty, \infty), and the range is [0,)[0, \infty).

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