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

Algebra
Tutor: None Selected Time limit: 1 Day

determine how the parabola has in common with the x-axis and whether its vertex lies above on or below the x-axis

y=4x^2-12x+12

Mar 10th, 2015

We can see from the fact that x^2 term is positive that the parabola goes to + infinity as |x| gets large (it forms a "u shape").

We can also rearrange this standard form quadratic (y = ax^2 + bx + c) into vertex form (y = a(x - h)^2 + k). Or, more quickly, use the formula:

k = c - (b^2 / 4a)

= 12 - (144/16)

= 12-9

= 3

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 up, it will not cross the x-axis.


Mar 10th, 2015

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