Question

Identify the graph of a quadratic equation with two different rational solutions.

u-shaped graph opening up and not crossing the axis

u-shaped graph opening down and touching the axis at (3, 0)

u-shaped graph opening up and crossing the x-axis at (−3, 0) and (2, 0)

u-shaped graph opening down and crossing the axis at approximately (−2.3, 0) and at approximately (1.3, 0)

Answer 1

Help me please

Answer 2

In order for a quadratic equation to have rational roots, it must cross the x-axis.
It will have 2 roots if it crosses the x-axis at 2 places.

Answer 3

Wht?

Answer 4

hello harlie basically it seems as though the answer could be the last 2 choices

Answer 5

oh

Answer 6

but how do i know if it is the right answer

Answer 7

All I know is that a quadratic equation will have 2 distinct rational roots if it crosses the x axis in two different places. It seems as though the last two choices meet that requirement.

Answer 8

I do see a difference. It is in the description if it is concave up or down. It would be much easier to tell if the equations were shown. If the x² coefficient is positive it is concave up (shaped like a 'u'). If the x² coefficient is negative it is concave down.

Answer 9

The key here is that the last 2 choices have "approximate" solutions. I think that is supposed to be telling you that those x-intercepts are not RATIONAL roots. E.g., the "approximately 1.3" might be and approximation for \(\sqrt{1.7}\).

The exact roots are clearly rational roots.

The type and number of roots don't have anything to do with opening up/opening down. If it crosses the x-axis twice, there ARE 2 real roots. The only question is whether they are rational or irrational.