I need a graph please

Question

 

c) Two turning point, a positive leading coefficient,one x intercept and a constant term of 3.

Answer 1

Graph the function with two turning point, a positive leading coefficient,one x intercept and a constant term of 3.

We know that if there are n turning points then the degree of the polynomial is (n+1) or more.

There are two turning points then the degree of the Equation can be 3 or greater.

Consider a Cubic Function

Now the function has one x-intercept,

then third degree equation is (x - a)(bx² + cx + d) = 0

Solving the Equation

bx³ + cx²+dx - abx² - acx - ad = 0

bx³ + (c - ab) x² + (d-ac) x - ad = 0

The cubic Function is bx³ + (c - ab) x² + (d-ac) x - ad = 0.

The Constant term is 3.

From the constant term from the cubic Equation is -ad

-ad = 3

ad = -3

Let us assume a = -3 and d = 1

The polynomial has positive leading coefficient which means b > 0

So Let us assume b = 1 and c = 2

Then Cubic Equation is

bx³ + (c - ab) x² + (d-ac) x - ad = 0

x³ + 5x² + 7x + 3 = 0

So the Cubic Equation is x³ + 5x² + 7x + 3 = 0

Graph

Therefore we can from the turning points are (-1,0) and (-2.33, -1.185) and x - intercept is (-3,0).