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  1. Subjects ›
  2. Algebra ›
  3. Question of the Day

Algebra Question of the Day

Algebra Question of the Day

Answer today's Algebra question, reveal the full explanation, then keep the streak going with a new question every day.

On a coordinate plane, graph y=x2+4x+3y=x^2+4x+3y=x2+4x+3. What are the xxx-intercepts (as points)?

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Question of the Day

On a coordinate plane, graph y=x2+4x+3y=x^2+4x+3y=x2+4x+3. What are the xxx-intercepts (as points)?

  1. (−1,0)(-1,0)(−1,0) and (−3,0)(-3,0)(−3,0) (correct answer)
  2. (1,0)(1,0)(1,0) and (3,0)(3,0)(3,0)
  3. (0,−1)(0,-1)(0,−1) and (0,−3)(0,-3)(0,−3)
  4. (−4,0)(-4,0)(−4,0) and (3,0)(3,0)(3,0)

Explanation: This question tests your understanding of how to identify key features of quadratic functions and their graphs, specifically x-intercepts. The x-intercept is where the graph crosses the x-axis, which always happens when y = 0: to find it, set your function equal to 0 and solve for x, giving you the point(s) (x-value, 0). To find the x-intercept(s), we set y = 0 and solve: 0 = x² + 4x + 3; factoring gives us (x + 1)(x + 3) = 0, so x = -1 and x = -3, giving us the points (-1, 0) and (-3, 0). Choice A is correct because it properly identifies the x-intercepts as (-1, 0) and (-3, 0) using factoring, with accurate solutions. Choice B gets the signs wrong: the factors are (x + 1) and (x + 3), which give negative roots -1 and -3, not positive 1 and 3. Quick trick for intercepts: for x-intercepts, set y = 0 and solve. And remember: intercepts are points with two coordinates, so write them as (x, y), not just single numbers.