Question

REVIEW:

Mai graphs the function p given by p(x) = (x + 1)(x-2)(x +
15) and sees this graph.
She says, "This graph looks like
a parabola, so it must be a
quadratic."
(a) Is Mai correct?
(b) Explain how you could select a
viewing window before graphing an
expression like p(x) that would
show the main features of a graph.
-10
ry
35
30
25
20
15
10
5
-15
-20
-25
-30
-35
-40

Answer 1

No, the graph is not a quadratic function but a cubic function. To select a viewing window for graphing such a function, consider the zeros of the function and choose a range that captures these main features.

Step-by-step explanation:

No, Mai is not correct. Although the graph of the function p(x) = (x + 1)(x-2)(x + 15) may look like a parabola, it is actually a cubic function. Quadratic functions have the general form y = ax^2 + bx + c, while cubic functions have the general form y = ax^3 + bx^2 + cx + d. The presence of the x^3 term in the function p(x) indicates that it is a cubic function, not a quadratic one.

When selecting a viewing window for graphing a function like p(x), it is important to choose a range that captures the main features of the graph. This can be done by considering the zeros of the function, which are the x-values where the function intersects the x-axis. In this case, the zeros are -1, 2, and -15. A suitable viewing window could be a range of x-values from -20 to 5, which includes these zeros and allows for a clear visualization of the graph.

Learn more about Quadratic vs. cubic functions