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
7.5k points