SOLUTION: how do you know when there is an x intercept? for example, it says: For each example, find the vertex, the axis of symmetry, the y intercept, the x intercepts if any, and graph. (T

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: how do you know when there is an x intercept? for example, it says: For each example, find the vertex, the axis of symmetry, the y intercept, the x intercepts if any, and graph. (T      Log On


   

Question 442014: how do you know when there is an x intercept? for example, it says: For each example, find the vertex, the axis of symmetry, the y intercept, the x intercepts if any, and graph. (This is the problem: y=1/2(x+3)^2-1
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Note: vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

y=1/2(x+3)^2-1  |a = .5 > 0  Parabola opens upward.

Vertex(-3,-1) Line of symmetry is x = -3

 y = .5*9-1 when x = 0  y-intercept is (0,7/2)

 0 = .5(x+3)^2 - 1

 2 = (x+3)^2

 ±sqrt%282%29-3 = x when y = 0  x-intercepts are (-4.4142,0) and (-1.5858, 0)









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