Which of the following correctly describes the end behavior of the polynomial
1 answer:
Answer:
A. Both ends go down.
General Formulas and Concepts:
<u>Algebra II</u>
- End behavior - what the y-values are approaching as x approaches negative infinity or infinity
Step-by-step explanation:
If we graph the function, we can see that when x goes to -∞, y also goes to -∞.
We also see that when x goes to ∞, y <em>still</em> goes to -∞.
Therefore, both ends of the graph would head towards -∞, making A. the correct answer choice.
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The vertex-form equation is
y = a(x+1)² -16
Putting in the y-intercept values, we have
-15 = a(0+1)² -16
1 = a . . . . . . . . . . . add 16
Then the x-intercepts can be found where y=0.
0 = (x+1)² -16
16 = (x+1)²
±4 = x+1
x = -1 ± 4 = {-5, 3}
y = a(x+1)² -16
Putting in the y-intercept values, we have
-15 = a(0+1)² -16
1 = a . . . . . . . . . . . add 16
Then the x-intercepts can be found where y=0.
0 = (x+1)² -16
16 = (x+1)²
±4 = x+1
x = -1 ± 4 = {-5, 3}