Sketching Polynomial Graphs Part 1

Step 1: Find zeros (x-intercepts)

Step 2: Find y-intercept, (substitute 0 in for x)

Step 3: Determine End Behavior

Step 4: Sketch the polynomial function by using Steps 1-3, and make a t-table(pick points in between zeros)

tack

 

Sticking Point: Remember your parent graphs when you are sketching!!!!

 

Example 1

Step 1:

Factor: x(x + 2)= 0

Identify zeros: x = 0, x = -2

Step 2:

y-intercept = (0,0)

Step 3:

End Behavior:

n is even, a > 0

Therefore: as x -> +∞, f(x) -> +∞ and x -> -∞, f(x) -> +∞

Step 4:

Sketch the polynomial function.

Plot Zeros, End Behavior, and remember Parent Graph:

sketch of polynomial

 

Example 2

Step 1:

Factor:

Identify zeros: x = 0, x = -1, x = 1

 

Step 2:

y-intercept (0,0)

Step 3:

End Behavior:

n is odd, a > 0

Therefore: as x -> +∞, f(x) -> +∞ and x -> -∞, f(x) -> -∞

Step 4:

Sketch the polynomial function. Plot Zeros, End Behavior, and remember Parent Graph

sketch of polynomial

 

Example 3

Step 1:

Factor:

Identify Zeros:

x =0, x = 3, x = -1

Step 2:

y-intercept (0,0)

Step 3:

End Behavior:

n is odd, a < 0

Therefore: as x -> +∞, f(x) -> -∞ and x -> -∞, f(x) -> +∞

Step 4:

Sketch the polynomial function. Plot Zeros, End Behavior, and remember Parent Graph

sketch of polynomial

 

Need to see more examples? Watch the video below on how to graph polynomials