5.4k views
2 votes
Find the equation of a quadratic function with the given zeros -1 and 3 and contains the given point (1, 4). Express each function in factored form.

User Jefferson
by
7.6k points

1 Answer

3 votes

To find the equation of a quadratic function with given zeros and a point, you can start by using the zero-factor theorem. If the zeros are -1 and 3, then the factors of the quadratic equation are (x + 1) and (x - 3).

Now, we can write the equation in factored form:

f(x) = a(x + 1)(x - 3)

To determine the value of 'a,' we can use the given point (1, 4):

f(1) = 4

Substituting this into the equation:

4 = a(1 + 1)(1 - 3)

4 = a(2)(-2)

Now, solve for 'a':

4 = -4a

Divide both sides by -4:

a = -1

So, the equation of the quadratic function in factored form is:

f(x) = -1(x + 1)(x - 3)

You can leave it in this factored form or expand it if needed:

f(x) = -1(x^2 - 2x - 3)

f(x) = -x^2 + 2x + 3

This is the equation of the quadratic function with the given zeros (-1 and 3) and the point (1, 4).

User Michaelrccurtis
by
8.7k 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