SOLUTION: y=1/2x^2+x-4 Sketch the following quadratic relationship by finding the x-intercepts , the y intercept, axis of symmetry, mirror of the y intercept and the vertex

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: y=1/2x^2+x-4 Sketch the following quadratic relationship by finding the x-intercepts , the y intercept, axis of symmetry, mirror of the y intercept and the vertex      Log On


   

Question 1118926: y=1/2x^2+x-4
Sketch the following quadratic relationship by finding the x-intercepts , the y intercept, axis of symmetry, mirror of the y intercept and the vertex
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


y=%281%2F2%29x%5E2%2Bx-4

Factor out the leading coefficient and complete the square in x to find the vertex and axis of symmetry.

y+=+%281%2F2%29%28x%5E2%2B2x-8%29
y+=+%281%2F2%29%28x%5E2%2B2x%2B1-9%29
y+=+%281%2F2%29%28%28x%5E2%2B2x%2B1%29-9%29
y+=+%281%2F2%29%28%28x%2B1%29%5E2%29-9%2F2

The vertex is (-1,-9/2); the axis of symmetry is x=-1.

The y-intercept is where x=0; setting x=0 in the original form of the equation we see the y-intercept is (0,-4).

Then since the axis of symmetry is x = -1, the mirror of the y-intercept is (-2,-4).

To find the x-intercepts (the zeros of the function), the easiest way is to look at the original equation after the leading coefficient has been factored out:

y+=+%281%2F2%29%28x%5E2%2B2x-8%29
y+=+%281%2F2%29%28x%2B4%29%28x-2%29

The zeros are -4 and +2; the x-intercepts are (-4,0) and (2,0).

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%281%2F2%29x%5E2%2Bx-4%29