Question

Write a quadratic f whose zeros are -3 and 6

Answer 1

Given:

Zeros of the function = -3 and 6

Let's write a quadratic function with the given zeros.

Since the zeros are -3 and 6, we have:

x = -3

x = 6

Now, equate the zeros to zero:

• x = -3

Add 3 to both sides:

x + 3 = -3 + 3

x + 3 = 0

• x = 6

Subtract 6 from both sides:

x - 6 = -6 + 6

x - 6 = 0

Using the zeros, we now have the function:

$f(x)=(x+3)(x-6)$

Now, write the expression in standard form.

Expand using FOIL method and apply distributive property:

$\begin{gathered} f(x)=x(x-6)+3(x-6) \\ \\ f(x)=x(x)+x(-6)+3(x)+3(-6) \\ \\ f(x)=x^2-6x+3x-18 \\ \\ f(x)=x^2-3x-18 \end{gathered}$

Therefore, the function is:

$f(x)=x^2-3x-18$

ANSWER:

$f(x)=x^{2}-3x-18$