Question

y=x^2-7x+12
does the parabola open upward or downward..and how can i determine this?

Answer 1

This parabola opens upward.

Answer 2

If the first term is positive then the parabola is facing upward. If the first term is negative the parabola is facing downwards.

Answer 3

by completing the square, you can arrange it into the general parabola equation:

p(x) = a(x - h)^2 + k, where the vertex is at (h, k) and a describes the opening.

for a > 0, it opens upwards, for a < 0, it opens downwards. The larger |a| is, the steeper the parabola is.

so completing the square gives:

y = (x - (7/2))^2 + (97/4)

a = 1 and it is greater than 0.

therefore it opens upwards

Answer 4

@Euler271 @stardogchampion thank you both so much!