Question

Write a quadratic function f whose zeros are - 7 and -5.f(x) = 0

Answer 1

If a quadratic function f(x) equals 0, it will be of the form:

$ax^2\text{ + bx + c = 0.}$

The zeros of f(x) ( in this case, -7 and -5) are the values of x that will make f(x) become zero.

Therefore:

$\begin{gathered} x\text{ = -7 or x = -5} \\ x\text{ + 7 = 0 or x + 5 = 0} \\ \text{This means that if we multiply (x + 7) and (x+5) together, we should still get 0} \\ \text{This is because x+7 = 0 and x + 5 = 0. } \\ i\mathrm{}e\text{. 0}\times0\text{ = 0} \end{gathered}$

Therefore, to get the equation:

$\begin{gathered} (x+7)(x+5)\text{ =} \\ x^2\text{ + 5x + 7x + 35} \\ x^2\text{ + 12x + 35} \end{gathered}$$\begin{gathered} \text{The quadratic function f is:} \\ f(x)=x^2\text{ + 12x + 35} \end{gathered}$