without drawing the graph of the equation, determine how many points the parabo.

Question Description

I’m studying for my Algebra class and don’t understand how to answer this. Can you help me study?

determine how many points the parabola has in common with the x-axis and whether its vetex lies above on or below the x axis.


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Final Answer

We can see from the fact that x^2 term is negative that the parabola goes to -infinity as |x| gets large (it forms an inverted-u shape).

We can also rearrange this standard form quadratic (y = ax^2 + bx + c) into vertex form (y = a(x - h)^2 + k):


= -2(x^2 -x/2 +3/2)

= -2(x - 1/4)^2 + 3/2-1/16

Since (h,k) is the vertex we just need to check whether k is positive or negative. It is positive, so the vertex lies above the x-axis. And since the parabola curves down, it will cross the x-axis at two points.

iainharlow (1041)
Carnegie Mellon University

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