16.6k views
5 votes
Write a quadratic function that has x-intercepts (-3,0) and (4.0) and passes through the point (5,8)

1 Answer

3 votes

Final answer:

To find the quadratic function that satisfies the given conditions, we can use the x-intercepts and a point to set up a system of equations and solve for the coefficients.

Step-by-step explanation:

To find the quadratic function that satisfies the given conditions, we can start by writing the general form of a quadratic function: y = ax^2 + bx + c. Since we know that the function passes through the point (5,8), we can substitute these values into the equation and solve for a, b, and c: 8 = a(5)^2 + b(5) + c

Next, we can use the x-intercepts (-3,0) and (4,0) to set up two additional equations:

0 = a(-3)^2 + b(-3) + c

0 = a(4)^2 + b(4) + c

Solving this system of equations, we find that a = 1/7, b = -1/7, and c = 77/7. Therefore, the quadratic function that satisfies the given conditions is y = (1/7)x^2 - (1/7)x + 11.

User Emgee
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