30.3k views
0 votes
Write a function that has constant second differences, first differences that are not constant, a y-intercept of 2, and passes the point at (-16,3).

User Pforhan
by
7.3k points

1 Answer

4 votes

Final answer:

To write a function that has constant second differences, first differences that are not constant, a y-intercept of 2, and passes through the point (-16,3), we can use a quadratic function. By substituting the given point into the function and solving for the coefficients, we can find the specific function that meets the requirements.

Step-by-step explanation:

To write a function that has constant second differences, first differences that are not constant, a y-intercept of 2, and passes through the point (-16,3), we can use a quadratic function. A quadratic function is in the form y = ax^2 + bx + c. Since we want constant second differences, the coefficient of x^2 should be 0. To find the coefficients a, b, and c, we can substitute the given point into the function and solve for the coefficients.

Given the point (-16,3), we have 3 = a(-16)^2 + b(-16) + c. Plugging in the value of x and y into the equation, we get 3 = 256a - 16b + c. Since we want the y-intercept to be 2, we have c = 2. Substituting c = 2 into the equation, we have 3 = 256a - 16b + 2. Simplifying the equation, we get 1 = 256a - 16b. Since we want first differences that are not constant, we can choose any values for a and b as long as they satisfy the equation. For example, we can choose a = 1 and b = -15.

Therefore, the function that satisfies the given conditions is y = x^2 - 15x + 2.

User Spunge
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories