[ASK] c and q

Algebra

[ASK] c and q

Postby Monox D. I-Fly » Sun Aug 23, 2020 10:40 pm

The graph's turning point of a quadratic function [tex]f(x)=ax^2+bx+c[/tex] 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
 
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Re: [ASK] c and q

Postby Guest » Mon Aug 24, 2020 2:02 am

over the [tex]x[/tex]-axis, it could mean two things. it could mean on the [tex]x[/tex]-axis or it could mean above the [tex]x[/tex]-axis

if it means on the [tex]x[/tex]-axis

then [tex]B[/tex] and [tex]D[/tex] are correct

if it means above the [tex]x[/tex]-axis

[tex]B[/tex] is correct


the value of [tex]c[/tex] is the value of [tex]y[/tex] when [tex]x = 0[/tex] (the point when the function crosses the y-axis)

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

---------
when [tex]a > 0[/tex] and the turning point on the [tex]x[/tex] axis or above it
[tex]c[/tex] is positive

when [tex]a > 0[/tex] and the turning point below the [tex]x[/tex] axis
[tex]c[/tex] could be positive or negative

when [tex]a < 0[/tex] and the turning point on the [tex]x[/tex] axis or below it
[tex]c[/tex] is negative

when [tex]a < 0[/tex] and the turning point obove the [tex]x[/tex] axis
[tex]c[/tex] could be positive or negative


-Jambo 8)
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Re: [ASK] c and q

Postby Monox D. I-Fly » Mon Aug 24, 2020 10:37 pm

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

Monox D. I-Fly
 
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