Algebra

The graph's turning point of a quadratic function $$f(x)=ax^2+bx+c$$ is over the X-axis. If the coordinate of the turning point is (p, q) and a > 0, the correct statement is ....

A. c is less than zero

B. c is more than zero

C. q is less than zero

D. q equals zero

Since the point (p, q) is over the X-axis that means q is more than zero, so the options C and D are out of question. What should I do to determine if c is positive or negative? I'm stuck on this. Thanks.
Monox D. I-Fly

Posts: 20
Joined: Tue May 22, 2018 1:38 am
Reputation: 3

over the $$x$$-axis, it could mean two things. it could mean on the $$x$$-axis or it could mean above the $$x$$-axis

if it means on the $$x$$-axis

then $$B$$ and $$D$$ are correct

if it means above the $$x$$-axis

$$B$$ is correct

the value of $$c$$ is the value of $$y$$ when $$x = 0$$ (the point when the function crosses the y-axis)

since $$a > 0$$ and the function above x-axis, it must cross the positive y-axis (c is positive)

---------
when $$a > 0$$ and the turning point on the $$x$$ axis or above it
$$c$$ is positive

when $$a > 0$$ and the turning point below the $$x$$ axis
$$c$$ could be positive or negative

when $$a < 0$$ and the turning point on the $$x$$ axis or below it
$$c$$ is negative

when $$a < 0$$ and the turning point obove the $$x$$ axis
$$c$$ could be positive or negative

-Jambo
Guest

By "over", I mean "above" so the answer is B. Thanks for your help, Jambo!

Monox D. I-Fly

Posts: 20
Joined: Tue May 22, 2018 1:38 am
Reputation: 3