154k views
0 votes
Write a quadratic function given the roots (3, 0) and (1, 0) and the point (4, 9).

1 Answer

4 votes

Final answer:

To write the quadratic function with given roots (3, 0) and (1, 0) and a point (4, 9), we start with the factored form y = a(x - 3)(x - 1), substitute the point to find 'a', and then expand to obtain y = 3x^2 - 12x + 9.

Step-by-step explanation:

The student has asked how to write a quadratic function given the roots (3, 0) and (1, 0), and a point (4, 9). Since the roots are known, the quadratic function can be written in factored form as

y = a(x - 3)(x - 1),

where 'a' is a constant that we need to determine. By using the given point (4, 9), we can substitute the x and y values into the equation to solve for 'a':

9 = a(4 - 3)(4 - 1),

9 = a(1)(3),

9 = 3a,

a = 3.

Now we have the quadratic function:

y = 3(x - 3)(x - 1).

This can be expanded to get the standard form of the quadratic equation:

y = 3(x^2 - 4x + 3),

y = 3x^2 - 12x + 9.

User Moeri
by
8.1k 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