Math true or false

Question

A. If a quadratic function has at least one real zero and the vertex of its graph is (3,-5), then the graph of the function is a parabola that opens down.

 

B. Suppose that the function y=f(x) is increasing on the interval (-1,5). Then the graph of y=-f(x) is also increasing on (-1,5).

 

C. For a constant function, the average rate of change is zero.

 

Please help determine if true or false and explain your thinking.

Thanks!

Answer 1

A. False because a zero is a point where the value of y is zero. Graphically speaking, the graph should touch the x-axis. Plotting that vertex, you can see that the only way for it to intersect the x-axis is to go up.

 

B. False. If you're on calculus already, putting a negative in the entire function will make the value of the entire slope (which is the first derivative of the function) opposite in sign compared to the one without the negative. A positive slope means the value is increasing at that point while a negative slope means decreasing. However if you're not in calculus yet, you can simply show this through example such as f(x) = x & f(x) = -x, or using parabolas while putting the line of symmetry on either invervals (because you need to fulfill the conditions).

 

C. True. This is self-explanatory. It's constant so there's no change. Technically speaking (again if you're on calculus), it's saying that "The slope of a constant function is 0." which is always true.

 

NOTE: If you're just up to second degree equations (parabolas), you don't really need to know calculus to understand what I was talking about on slopes. I just said those because slopes will still apply for higher degrees of functions.