46.8k views
2 votes
Determine the equation of a quadratic function whose roots are - 3 and 4 and which passes through the point (5, 40)

User Aalaap
by
8.4k points

1 Answer

3 votes

Final answer:

The equation of the quadratic function with roots -3 and 4 that passes through the point (5, 40) is y = 5x^2 - 5x - 60.

Step-by-step explanation:

To determine the equation of a quadratic function with roots -3 and 4 that passes through the point (5, 40), we can use the factored form of a quadratic equation ax2 + bx + c = 0. Since the roots are -3 and 4, the factored form of the equation is a(x + 3)(x - 4) = 0. To find the value of 'a', we use the given point (5, 40).

Plugging the point into the equation, we get: a(5 + 3)(5 - 4) = 40. This simplifies to 8a = 40, so a = 5. Now, we know the equation is y = 5(x + 3)(x - 4).

After expanding, the quadratic equation is: y = 5x2 - 5x - 60. This is the standard form of the quadratic equation we were looking for.

User Pooran
by
8.2k 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