analyzing the relationship between the vertex and y - intercept of a quadratic function\nwhich must be true…
analyzing the relationship between the vertex and y - intercept of a quadratic function\nwhich must be true of a quadratic function whose vertex is the same as its y - intercept?\nthe axis of symmetry for the function is x = 0.\nthe axis of symmetry for the function is y = 0.\nthe function has no x - intercepts.\nthe function has 1 x - intercept.
Answer
Explanation:
Step1: Recall quadratic - function properties
The vertex - form of a quadratic function is (y=a(x - h)^2+k), where ((h,k)) is the vertex. The (y) - intercept is found by setting (x = 0), so (y=a(0 - h)^2+k=ah^{2}+k). If the vertex ((h,k)) is the same as the (y) - intercept, then when (x = 0), (y=k). Substituting (x = 0) into (y=a(x - h)^2+k) gives (y=ah^{2}+k), so (ah^{2}=0). Since (a\neq0) (otherwise it's not a quadratic function), (h = 0).
Step2: Recall the axis - of symmetry formula
The axis of symmetry of a quadratic function (y=a(x - h)^2+k) is given by the equation (x = h). Since (h = 0) (from Step 1), the axis of symmetry is (x = 0).
Answer:
The axis of symmetry for the function is (x = 0).