Math  /  Algebra

QuestionFor the quadratic function f(x)=x2+2x+1f(x)=x^{2}+2 x+1, answer parts (a)(a) through ( ff ). (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 x-intercepts, if any. Select the correct choice below and, if necessary, fill in the answer box to comp your choice. A. The xx-intercept(s) is/are -1 . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no x-intercepts.
What is the y-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The yy-intercept is 1 . (Type an integer or a simplified fraction.) B. There is no yy-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 (,)(-\infty, \infty). (Type your answer in interval notation.) The range of ff is [0,)[0, \infty). (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval \square (Type your answer in interval notation.)

Studdy Solution
The function is increasing and decreasing based on the axis of symmetry.
Since the graph is concave up and the axis of symmetry is x=1 x = -1 :
- The function is decreasing on (,1) (-\infty, -1) . - The function is increasing on (1,) (-1, \infty) .
The solution to each part of the problem is as follows: - Axis of symmetry: x=1 x = -1 - Concavity: Concave up - y y -intercept: (0,1) (0, 1) - x x -intercept: (1,0) (-1, 0) - Domain: (,) (-\infty, \infty) - Range: [0,) [0, \infty) - Increasing on: (1,) (-1, \infty) - Decreasing on: (,1) (-\infty, -1)

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