SOLUTION: Find the vertex and intercepts for each quadratic function. Does it open up or down? y = x^2 – 4

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Find the vertex and intercepts for each quadratic function. Does it open up or down? y = x^2 – 4       Log On


   

Question 4114: Find the vertex and intercepts for each quadratic function. Does it open up or down? y = x^2 – 4
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
There are several ways to find the vertex and graph a quadratic function. One easy way is to realize that in the general case
+y+=+ax%5E2+%2B+bx+%2B+c+
the vertex is at
+x=+-b%2F2a+
Therefore for y+=+x%5E2+-+4 the coefficient of x is zero, so the vertex is at x=0. When x = 0, y = -4, so the vertex is at (0, -4).

The graph opens upward, since the coeffient of x^2 is positive. It would open downward if the coefficient of x^2 is negative.

The y-intercept is where x=0, which is at the point (0, -4).

The x-interecepts are where y=0, which are at
0=x%5E2+-+4 or x=2 and at x=-2.