Studdy AI Logo
Math  /  Algebra

QuestionThe table defines a quadratic function. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-1 & 5 \\ \hline 0 & 1 \\ \hline 1 & -1 \\ \hline 3 & 1 \\ \hline \end{tabular}
What is the average rate of change between x=−1x=-1 and x=1x=1 ? (a) undefined (b) −13-\frac{1}{3} (C) -3 (d) -4

Studdy Solution

STEP 1

1. The table represents a quadratic function.
2. The average rate of change between two points on a function is calculated using the slope formula for those points.

STEP 2

1. Identify the points from the table corresponding to x=−1 x = -1 and x=1 x = 1 .
2. Use the slope formula to calculate the average rate of change.
3. Compare the calculated rate of change to the given options.

STEP 3

Identify the points from the table:
For x=−1 x = -1 , y=5 y = 5 . So the point is (−1,5)(-1, 5).
For x=1 x = 1 , y=−1 y = -1 . So the point is (1,−1)(1, -1).

STEP 4

Use the slope formula to find the average rate of change between the two points. The slope formula is:
Slope=y2−y1x2−x1 \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the points (−1,5)(-1, 5) and (1,−1)(1, -1):
Slope=−1−51−(−1) \text{Slope} = \frac{-1 - 5}{1 - (-1)}

STEP 5

Simplify the expression:
Slope=−1−51+1 \text{Slope} = \frac{-1 - 5}{1 + 1} Slope=−62 \text{Slope} = \frac{-6}{2} Slope=−3 \text{Slope} = -3

STEP 6

Compare the calculated average rate of change to the given options:
The calculated average rate of change is −3-3, which corresponds to option (C).
The average rate of change between x=−1 x = -1 and x=1 x = 1 is:
−3 \boxed{-3}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord