# Determining c in Quadratic Function Turning Point

• MHB
• Monoxdifly
In summary: My apologies. In summary, 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 ...
Monoxdifly
MHB
The graph's turning point of a quadratic function $$\displaystyle f(x)=ax^2+bx+c$$ 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.

hint ...

what does the sign of the discriminant say about a quadratic’s roots?

If it's positive, it has two real roots. Okay, so D > 0.

D > 0
$$\displaystyle b^2-4ac>0$$
$$\displaystyle b^2>4ac$$
$$\displaystyle 4ac<b^2$$
$$\displaystyle c<\frac{b^2}{4a}$$
A square number must be positive, so $$\displaystyle b^2$$ is positive. Since a > 0 then 4a > 0, so $$\displaystyle \frac{b^2}{4a}$$ is still positive.
There's still a possibility that c is either negative or positive. What should I do next?

you were given $a>0$ which means the graph of the resulting parabola opens upward.
you were also given that the vertex of the parabola, $(p,q)$ was over the x-axis, hence $q > 0$.

If $q > 0$, the parabola has no x-intercepts ... the given quadratic has no real roots $\implies b^2-4ac <0$

"Over the x-axis" seems to me a strange way of saying "above the x-axis".

Country Boy said:
"Over the x-axis" seems to me a strange way of saying "above the x-axis".

I took it to be one of the three possibilities ... over, on, or under.

@skeeter:
Ah, I see. Thanks for your help.

@Country Boy:
Sorry, I didn't know the proper term so I came up with what I had in mind at best, without realizing that the simple "above" is already the proper term.

## 1. What is the formula for determining the turning point of a quadratic function?

The formula for determining the turning point of a quadratic function is (-b/2a, c-b^2/4a), where a, b, and c are coefficients in the general form of a quadratic function f(x) = ax^2 + bx + c.

## 2. How do you find the value of c in a quadratic function turning point?

The value of c in a quadratic function turning point can be found by substituting the x-coordinate of the turning point into the original quadratic function. This will give you the y-coordinate, which is the value of c.

## 3. Can you determine the turning point of a quadratic function without knowing the value of c?

Yes, it is possible to determine the turning point of a quadratic function without knowing the value of c. This can be done by using the formula -b/2a to find the x-coordinate of the turning point, and then substituting this value into the original function to find the y-coordinate.

## 4. What does the turning point of a quadratic function represent?

The turning point of a quadratic function represents the vertex of the parabola. It is the highest or lowest point on the curve, depending on whether the function opens upward or downward.

## 5. Can a quadratic function have more than one turning point?

No, a quadratic function can only have one turning point, which is the vertex of the parabola. This is because a quadratic function is a second-degree polynomial, meaning it can only have one maximum or minimum value.

Replies
6
Views
1K
Replies
3
Views
1K
Replies
4
Views
1K
Replies
16
Views
4K
Replies
2
Views
979
Replies
3
Views
2K
Replies
4
Views
4K
Replies
1
Views
2K
Replies
4
Views
2K
Replies
8
Views
2K